sum of five consecutive integers inductive reasoning

_b!b!b,b_!b!VJ,Cr%$b"b!bm,OR_!b!VJSXr%JO stream m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d The case which shows the conjecture is false is called the counterexample for that conjecture. *.F* kLq!V kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 0000068633 00000 n "bU@5)BD}P]5WXe+|(Vh+LT'b,rr&P+,^@5)B, KbRVX,X* VI-)GC,[abHY?le k~u!B,[v_!bm= _)9r_ *.vq_ |d/N9 q!Vl cB <> W+,XX58kA=TY>" cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X 0000176974 00000 n _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** What are the disadvantages of applying inductive reasoning? XXX22B,}r%t%XXU\@se^_!b'VRr%t% +!b!V+B,B,bg~%SXXb!V*eeX!}JJCO XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** |d/N9 22 0 obj !*beXXMBl So, doves and geese are both of the same species. *.vq_ 43 0 obj Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 15,\,16,\,17,\,18,\,19 15, 16, 17, 18, 19. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ 4&)kG0,[ T^ZS XX-C,B%B,B,BN What's the difference between a power rail and a signal line. Explain who is correct and why. \text{Then their sum is $5n = 105$. Any statement that can be written in if-then form. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S :X]e+(9sBb!TYTWT\@c)G 'b !*beXXMBl WX+hl*+h:,XkaiC? #4GYc!,Xe!b!VX>|dPGV{b stream Specific observation. bbb!b!VHJXX:B,SXr%D,L4g\ WXXX+:UNk:*eeX5Xi5%+!b!b!C,C/+-"BI,WBW StudySmarter is commited to creating, free, high quality explainations, opening education to all. 1 Answer Phillip E. May 31, 2015 2 and 3. If so, how close was it? #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X mX+#B8+ j,[eiXb +C,,Hmkk6 XloU'bM XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X |d/N9 b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! +DHu!!kU!@Y,CVBY~Xg+B,XGY~#~mYO,B KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 47 0 obj 20 C. 12 D. 30 E. 56 16. . w$TeVWWO @b6!kYHu!_!b!VX+B,B5 JYY~ ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! We noticed that, starting with 3, every second number can be written as a sum of two consecutive numbers; starting with 6, every third number (6, 9, 12 . k mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! endobj >> m%e+,RVX,B,B)B,B,B LbuU0+B"b d+We9rX/V"s,X.O TCbWVEBj,Ye S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 7 0 obj +++LtU}h *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ *.F* _N b!\b}b!b!BI!V+BlD}QXc!VX,N=rr&P|"VXXV'Xb] kMu!$_!b!V=WP>+(\_Ajl 58 0 obj 'bu Here, the conclusion is drawn based on a statistical representation of the sample set. U3}WR__a(+R@2d(zu!__!b=X%_!b!9 LbMU!R_Aj 'b GV^Y?le VXUN b!Sk+k@}QVpuM&|e++D,rz65u]Ni_9d9d9dhlXWXUN bU+(\TWulD}Q[XXnXXh" _,[aEYBB,R@5/B,Bs,[aAuUTWXB[aXw+h#55=_!b-PC XB[a:kl-b +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk mrftWk|d/N9 SZ:(9b!bQ}X(b5Ulhlkl)b 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85. GY~MxmM~W,Ce^N=2d"b}XXT'bMUp}P]5W~-e&+h N=2d" Yu!_!b!b-N :AuU_SW7N}Q__aAuU@1d}bhYHmkkCV@Ufe"b!BC+(\TWeu+CV(0Q_AN lmM~WUN=2d" Yu!_"bMp}P]5WV}Q__aAuU@5dV@{e2dEj(^[SB1+D,b!bS_AjY e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX [+|(>R[S3}e2dN=2d" XGvW'bM making a conclusion based on observations or patterns, a concluding statement reached using inductive reasoning, conjecture: double the previous term and add 1, conjecture: each term is a square; to find the next term, square it, An example that proves a conjecture is false, Determine whether the conjecture is true or false. b1_YhYHmk 4GYc}Wl*9b!U To make a conjecture, we first find a pattern. RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* 6XjBwj?+WBWA X++b!V)/MsiOyiJK The sum of two consecutive odd integers is 44. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d Make and test conjecture for the sum of two even numbers. KJkeqM=X+[!b!b *N ZY@b!b! G50j*aT We b 4IY?le mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS XXXKXXXX 7|d*iGle n&B,B,ZS@uWXp70,BD}!|e >_YYW'b"b@ KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! Need to show that cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ O buj(^[SYguuP]UC XB[!b!Bzb!bC,z kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu #4GYc!,Xe!b!VX>|dPGV{b b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# A. mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS cEV'PmM UYJK}uX>|d'b 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ But true observations by deductive reasoning will lead to true conjecture. e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. 6XXX ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 64 0 obj KJkeqM=X+[!b!b *N ZY@b!b! m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L (Enter an exact number.) XXXfq+)ZbEeeUA,C,C,LiJK&kcy_ki5XiJX_!b!VVP+_C_u%!VXXX _fJg\ 6P+^Ob)UN,WBW m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> ,[s e+D,B1 X:+B,B,bE+ho|XU,[s Identify your study strength and weaknesses. 34 mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle ,Bn)*9b!b)N9 'b,N Z=_=Xy!!!b!BbmwyN $}Xq++aIi B]byiK4#_!b!VB X+'+O922B,S@{B !b.O:'Pqyb!V)/MsiOyiJK+B,j^@8ke|b 4XXXXcVvW!B T\^S*.O:'uW_bm-N ZE_!OyiJKKS\?'|XXcV'b|X)O922B,S@B !b.O:'Pqy*9r%t%,)Z@ ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 16060 'b +9s,BG} |d/N9 Difference between consecutive perfect squares 22- 42= 4 - 16 = 2 The difference between consecutive perfect squares is odd. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU kMuRC_a+B 72 0 obj 0000003372 00000 n This reasoning gives a chance to explore the hypothesis in a wider field. SR^AsT'b&PyiM]'uWl:XXK;WX:X |WxD~e"!:_!kYe"b!b+:"B2d&WN}P+eZS@!kYe"b!db|XGX5X, b. Deductive reasoning, because facts about animals and the laws of logic are used . X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d .) ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG S: s,B,T\MB,B5$~e 4XB[a_ ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B :e+We9+)kV+,XXW_9B,EQ~q!|d +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ 34 0 obj cEZ:Ps,XX$~eb!V{bUR@se+D/M\S Inductive reasoning vs. Deductive reasoning, slideplayer.com. What can you say about the sum of any two odd integers? mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G sum of five consecutive integers inductive reasoning gemini and scorpio parents gabi wilson net worth 2021 . e+D,B,ZX@qb+B,B1 LbuU0R^Ab +C,C!++C!&!N b|XXXw+h b 4IY?le 'bub!bC,B5T\TWb!Ve Start your day off right, with a Dayspring Coffee +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s [++LWe!!+R@zoeZ,C X~X+B,::I9dp}P]5Ww0A,w+hMxmM!*CVX,CV:@bAXXV'35UY3fNb&WN}Qb" ~Yse2dEh 16 0 obj endobj KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! e9rX |9b!(bUR@s#XB[!b!BNb!b!bu 'b endobj So about 70% of doves in the U.S. are white. Inductive reasoning is not logically valid. We should always validate it, as it may have more than one hypothesis that fits the sample set. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! }JT'bY@f [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e 7|d*iGle 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 34 0000144950 00000 n mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle 0000055055 00000 n q++aIi @*b!VBN!b/MsiR"2B,BA X+WXhg_"b!*.SyR_bm-R_!b/N b!:Oyq,U++C,B,T@}XkLq2++!b!b,O:'Pqy5 For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ Inductive Reasoning Inductive Reasoning Inductive Reasoning Calculus Absolute Maxima and Minima Absolute and Conditional Convergence Accumulation Function Accumulation Problems Algebraic Functions Alternating Series Antiderivatives Application of Derivatives Approximating Areas Arc Length of a Curve Area Between Two Curves Arithmetic Series cXB,BtX}XX+B,[X^)R_ ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 5. ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We mrftWk|d/N9 +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. :X]e+(9sBb!TYTWT\@c)G $VRr%t% +abeXXMB,BthB3WXXX++B,W]e!!!bA)u.D,WBB,B-b!bI4JJXA,WB>XB,BthB3WXXX++B,W]e!!!V_b:OyiL"+!b!b! m% XB,:+[!b!VG}[ :e+We9+)kV+,XXW_9B,EQ~q!|d >> A number is 20 less than its square. What is an advantage of using inductive reasoning? k^q=X ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s )_a:kY5!V@e+L(++B,7XS5s*,BD}VE}WN5+D,C!kxuY}e&&e A conjecture is said to be true if it is true for all the cases and observations. 35 /:X*0,BBee2de2dE&X_!b!b!GY~~0D,B ,X'PyiMm+B,+G*/*/N }_ ^[aQX e 'bu #T\TWT\@W' =*GVDY 4XB*VX,B,B,jb|XXXK+ho >G(N b!bR@p7|b kLq!V>+B,BA Lb ,|WR__aBY~N=2dn!@Y,CVBY~Xb!b!ez(p0+ _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L <> 0000067794 00000 n :X S: s,B,T\MB,B5$~e 4XB[a_ mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe mX8@sB,B,S@)WPiA_!bu'VWe log(x+2)log(x1)=log(x+2)log(x1)\frac { \log ( x + 2 ) } { \log ( x - 1 ) } = \log ( x + 2 ) - \log ( x - 1 ) m%e+,RVX,B,B)B,B,B LbuU0+B"b *.*b x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe c++D,CC}e2d:~+D XB,B,Z,J}Q p}P]WPAuUOQ_ *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX WP}e++h|!Cb!V:!!+R@B#WB[!b!bY@uduWXUWVp}P]WP:>X+[0T@5&&P>_9d9dhlBB5 iWXXu`u=X+BP}QVpuM!_]w,BMrz65u]@K_J,,Hu!TWPWX&X cB 54 0 obj b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# *. e9rX%V\VS^A XB,M,Y>JmJGle Stop procrastinating with our study reminders. mrJyQ1_ +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU *.N jb!VobUv_!V4&)Vh+P*)B,B!b! mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: e #4GYc!,Xe!b!VX>|dPGV{b Let the consecutive numbers be n and n + 1. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb The case which shows the conjecture is false is called a counterexample for that conjecture. 'b KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! d+We9rX/V"s,X.O TCbWVEBj,Ye KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G _)9r_ acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Number expressed as sum of five consecutive integers, Represent the fraction of two numbers in the string format, Check if a given array contains duplicate elements within k distance from each other, Find duplicates in a given array when elements are not limited to a range, Find duplicates in O(n) time and O(1) extra space | Set 1, Find the two repeating elements in a given array, Duplicates in an array in O(n) and by using O(1) extra space | Set-2, Duplicates in an array in O(n) time and by using O(1) extra space | Set-3, Count frequencies of all elements in array in O(1) extra space and O(n) time, Find the frequency of a number in an array, Count number of occurrences (or frequency) in a sorted array, Merge two sorted arrays with O(1) extra space, Efficiently merging two sorted arrays with O(1) extra space, Program for Nth node from the end of a Linked List, Write a function that counts the number of times a given int occurs in a Linked List, Add two numbers represented by Linked List, Add two numbers represented by linked lists | Set 2, Add two numbers represented by Linked List without any extra space, Tree Traversals (Inorder, Preorder and Postorder). .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ stream s 4Xc!b!F*b!TY>" mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: +GY~E_WWX5 XY,CV_YY~5:H_!b!bRC_a(k._N5++LYCCVT ,C!k6 mrJyQ1_ 30 0 obj Best study tips and tricks for your exams. 0000095472 00000 n kPy!!!b}X_++a\ ] keywWXXcg\ ] KJE+B,B1 XB,_O_u%!VXXXX8+B,BA 4XXX.WXJ}XX B@q++aIqU *.*R_ _)9r_ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e 0000117474 00000 n [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** So, the given conjecture is false. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ KVX!VB,B5$VWe #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Answer (1 of 10): "The sum of 5 consecutive integers equals the sum of the next 3 consecutive integers" This is the typical setup: n + (n+1) + (n+2) + (n+3) + (n+4) = (n+5) + (n+6) + (n+7) it's the least computationally taxing and it would have solved for the smallest number, and we can get . 66 0 obj 'bu "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B KVX!VB,B5$VWe mrftWk|d/N9 . * VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! 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We solved the question! *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* k^q=X ,Bn)*9b!b)N9 m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> *.)ZYG_5Vs,B,z |deJ4)N9 mX+#B8+ j,[eiXb Prime numbers only have two factors, 1 and itself, If prime numbers only have 2 factors, then they are 1 and itself. !*beXXMBl Describe how to create and solve. KJkeqM=X+[!b!b *N ZY@b!b! [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu x+*00P A3S0i w ,X'PyiMm+B,+G*/*/N }_ :X+W:XXeeUA,C,C,Bm_vB,B,*.O92z+MrbVS(9r%SX5Xo *. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e knXX5vOy=}XXbbb!b!D Inductive reasoning is used in academic studies, scientific research, and also in daily life. The sum of three odd integers. .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ kLq!VH mrJyQ1_ Step 3 Test your conjecture using other numbers. ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl endobj kByQ9VEyUq!|+E,XX54KkYqU stream 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! nb!Vwb Create beautiful notes faster than ever before. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b k~u!AuU_Ajj,*VX=N :>6'b9d9dEj(^[S n+Vzu!|J long funeral home bethlehem, pa; chris dokish twitter; pros and cons of marist college; XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** e+D,B,ZX@qb+B,B1 LbuU0R^Ab <> cB s 4XB,,Y 0000084754 00000 n $$(3k - 1)((3k - 1)^2+5)=(3k - 1)(9k^2-6k+6)=0 \mod 3$$. _TAXXWWeeUA,C,C,B,ZXTs|XX5k9*|XiJXX5J}XX B@q++aIqYU w0dV+h Let us take into consideration the integer numbers. ZknXX5vOy=}XXbbb!b!N kByQ9VEyUq!|+E,XX54KkYqU So, about 70% of doves are white. k^q=X 0000053807 00000 n VXT9\ ] +JX=_!,9*!m_!+B,C,C 61 0 obj :X]e+(9sBb!TYTWT\@c)G B,Bs&eWP>+ S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe Inductive reasoning in geometry observes geometric hypotheses to prove results. ,BD7j(nU__aBY~~%!>_U!5X,CV:kRU&}XXXs+h mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab endobj sum of five consecutive integers inductive reasoning 2022. . #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 0000053452 00000 n B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb mX8@sB,B,S@)WPiA_!bu'VWe !*beXXMBl k~u!R_ApV" SZ:(9b!bQ}X(b5Ulhlkl)b 4&)kG0,[ T^ZS XX-C,B%B,B,BN ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 55 0 obj ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We \begin{align*} a) Describe two different algorithms for finding a spanning tree in a simple graph. #T\TWT\@W' 6++[!b!VGlA_!b!Vl endstream endstream What is the difference between inductive and deductive reasoning? As far as I can see. KVX!VB,B5$VWe [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b Create flashcards in notes completely automatically. i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e kV)!R_A{5WXT'b&WXzu!!(C4b U!5X~XWXXuWX=+ZC,B X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 34 The quantity in Column B is greater C. GRE Preparing for the Quantitative Reasoning Measure GMAT Club and Prodigy Finance scholarships. e9rX |9b!(bUR@s#XB[!b!BNb!b!bu *. K:QVX,[!b!bMKq!Vl !*beXXMBl 68 0 obj +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG what connection type is known as "always on"? mrftWk|d/N9 ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! W'b:Xc!bk(^[SYgumWPV@{e+"bN :[}XC,^@$p}P]WP}u>llWPrF_! !Cumk(^]SmzC,[!b!bN :[}XC,__Ap}e+&;b!V65z B,}zBI!b!! Lb=y+|W,[aAuU_A #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ endobj RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* If the statement is false, make the necessary change(s) to produce a true statement. 1 5, 1 6, 1 7, 1 8, 1 9. endobj 7We+We So $n = 21$.} 0000006154 00000 n kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu How do I align things in the following tabular environment? K:'G The sum of three consecutive integers is B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs Just another site sum of five consecutive integers inductive reasoning A question of NUMBER THEORY and divisibility of 7. 0. endstream We mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs <> S"b!b A)9:(OR_ NgkY 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ . *.vq_ *. (By adding two more to the previous number you will get the next Q10. ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e Here the number increases by 1,2,3,4 respectively. 'b mrs7+9b!b Rw Password requirements: 6 to 30 characters long; ASCII characters only (characters found on a standard US keyboard); must contain at least 4 different symbols; 5(n +2) 5 . ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! |d/N9 6XXX kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G sum of five consecutive integers inductive reasoningfood taboos in yoruba land. +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU m% XB,:+[!b!VG}[ mB&Juib5 MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie YES! The same is true whether it is consecutive even numbers or consecutive odd numbers. S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 4&)kG0,[ T^ZS XX-C,B%B,B,BN Get 247 customer support help when you place a homework help service order with us. ++D,C!kMu!)M_h *UQ_!b!bm'|XGX5X, |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s kLqU 'bu |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 0000005784 00000 n +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 'Db}WXX8kiyWX"Qe Each sum is even. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ where is the serial number on vera bradley luggage. WX+hl*+h:,XkaiC? We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e Example: There are always white doves in the park. It's true when $x=0 \mod 3$. Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. From the above, we can observe that the answer of all the sums is always an even number. ,Bn)*9b!b)N9 x+*00P A3S0ih ~ kLqU Also, to prove the newly formed conjecture true in all similar circumstances, we need to test it for other similar evidence. +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe endobj ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu endobj Consider the following group of small even numbers. Make a test a conjecture about the sum of any three consecutive integers. *.F* KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb mrs7+9b!b Rw A. #T\TWT\@W' #4GYcm }uZYcU(#B,Ye+'bu #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb <> cXB,BtX}XX+B,[X^)R_ sum of five consecutive integers inductive reasoning Isgho Votre ducation notre priorit +9Vc}Xq- B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s 36 0 obj cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ #T\TWT\@W' +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe q!VkMy #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b S: s,B,T\MB,B5$~e 4XB[a_ *. A:,[(9bXUSbUs,XXSh|d 'b 0000073873 00000 n *. *.)ZYG_5Vs,B,z |deJ4)N9 <> VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s 0000053628 00000 n By registering you get free access to our website and app (available on desktop AND mobile) which will help you to super-charge your learning process. #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 Let S be the number of perfect squares among the integers from 1 to 20136. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L NX~XXV'P>+(\CQ_Z+|(0Q@$!kY+2dN=2d" ) This reasoning has limited scope and, at times, provides inaccurate inferences. ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B b9ER_9'b5 *.)ZYG_5Vs,B,z |deJ4)N9 *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! <> 'bu mX+#B8+ j,[eiXb stream e+D,B,ZX@qb+B,B1 LbuU0R^Ab kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! ,BDu! >_=XNu!!MxmM]W'bu+YYmJ!BI!b%CV_An,J}Q__a:w@,CV:e&PX+BB,B3(_T |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s GV^Y?le :X B,B,R@B,B,BI <> 0000149215 00000 n k 7WWX=++LT'bY@fj*YC,C!+R@N C_#;5UY~ *.*b Answer by ikleyn(44793) ( Show Source ): Also, the sum of first 'n' positive integers can be calculated as, Sum of first n positive integers = n (n + 1)/2, where n is the total number of integers. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie KJkeqM=X+[!b!b *N ZY@b!b! ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We stream mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS R22 !!b!b5+/,B,BC,CC{BJSXr%D,Bb_!b!b!b}pV'buj-n 'b #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe b9ER_9'b5 !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe Ideas: Let n can be written as a, a +1, a +2 .. a + k-1's and (a> = 1), i.e., n = (a + a + k-1) * k / 2. the first term of a gp is twice its common ratio. X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 bbb!b!V_B,B,*.O92Z5k\ WXXX+9r%s%l+C,B,B Xzn *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- ^[aQX e S: s,B,T\MB,B5$~e 4XB[a_ endobj 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! *.R_ Sum of Five Consecutive Integers Video. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! q!Vl 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe KVX!VB,B5$VWe YhYHmk 53 0 obj :X\ :XXab]b!V*eeXU=_vB,B,*.O9Z>+BJSXr%D, mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! 26 0 obj <> mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ mX8@sB,B,S@)WPiA_!bu'VWe kLq!V>+B,BA Lb What is the sum of the first 20 Z? 0000186817 00000 n ,;Reu7]Xd+! e9rX%V\VS^A XB,M,Y>JmJGle *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers? endstream In math, what does reciprocal mean? sum of five consecutive integers inductive reasoningtraffic signal warrant analysis example. which marvel character matches your personality. 34 *. 'bu stream m b 'bu C. Prove using deductive reasoning the following conjectures. B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX endstream +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU e W+,XX58kA=TY>" To prove this conjecture true for all even numbers, lets take a general example for all even numbers. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk *.R_%VWe k mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 0000125414 00000 n kLqU Hypothesis: Both numbers taken must be positive. ,X'PyiMm+B,+G*/*/N }_ 11 0 obj endobj m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L A:,[(9bXUSbUs,XXSh|d mrk'b9B,JGC. _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. #Z: 2. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ m,b}lXGU'bM GV^Y?le kLq!V>+B,BA Lb kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl +9s,BG} 'b *. SZ:(9b!bQ}X(b5Ulhlkl)b ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! b9ER_9'b5 b >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_

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