++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ 10 0 obj ?*'++a\ nsB,B,BN!VWO:XX_!bXXXX#|JJAC/ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b Consider the following group of small even numbers. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 69 0 obj m%e+,RVX,B,B)B,B,B LbuU0+B"b w,[0Q_AN O buj(^[S=d >_9d9dhlBB5 4X?+B,B,::AuU_A mrJyQ1_ wl|k^Mx rr,hlX_ XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe *.*b b1_YhYHmk You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case. 51 0 obj mrftWk|d/N9 EX . As we all know, even numbers are integers divisible by 2. 15 0 obj K:QVX,[!b!bMKq!Vl K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD This type of reasoning forms a causal connection between evidence and hypothesis. ?l Inductive reasoning is considered to be predictive rather than certain. cB * . MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe *.N jb!VobUv_!V4&)Vh+P*)B,B!b! So, doves and geese are both of the same species. The sum of 5 consecutive integers can be 100. ~+t)9B,BtWkRq!VXR@b}W>lE ~+t)9B,BtWkRq!VXR@b}W>lE *.vq_ The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. 'bul"b e 5(n +2) If we divide this sum of any 5 consecutive integers by 5 we get: 5(n + 2) 5 . q++aIi *b!VBN!b/MsiU"2B,BA X+WXhg_"b!*.SyU_bm-R_!b/N b!:Oyq\U++C,B,T@B,j_@seeX5&r% +!b!b)O:'Pq}Xkk}X8SXKS\?Ubbb!b!Bb!VC,C,C,B1+a\ kNy'bl'bbb!b\ +JXXsN Tr_!b/9r%t%,)r_!b/N b!:Oy}uXXXX8ke}XkL|JXA,WBB,S@5u*O wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U [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 log(x+2)log(x1)=log(x+2)log(x1)\frac { \log ( x + 2 ) } { \log ( x - 1 ) } = \log ( x + 2 ) - \log ( x - 1 ) Here these numbers are integers. 'Db}WXX8kiyWX"Qe A hypothesis is formed by observing the given sample and finding the pattern between observations. m% XB,:+[!b!VG}[ K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, 4&)kG0,[ T^ZS XX-C,B%B,B,BN 2 The product of three consecutive natural numbers can be equal to their sum. S"b!b A)9:(OR_ cB Consider groups of three consecutive numbers. 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ U}WCu &!t_}W[SSH+D,jXeb-X'bj *,BD[}P]WP:YmbYNw5e:,BBvUg?Y@udm k vegan) just to try it, does this inconvenience the caterers and staff? ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! XXX22B+3XXXh^4 JSXr%D^?s|+aEgV'bmb!V*eeXD,WBB,B 4XCF4JJXA,WBE8MXJPMq!b!b!z8B,E,C,C cEZ:Ps,XX$~eb!V{bUR@se+D/M\S WX+hl*+h:,XkaiC? After understanding the concept of continuous integers, we use N to represent the first integer, then the second to 5th integers can be expressed as: N + 1, N + 2, N + 3 and N + 4. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 22 0 obj :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e which shows that n is sum of ve consecutive integers. What is the third number? mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ >> ~+t)9B,BtWkRq!VXR@b}W>lE 0000073513 00000 n endobj 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: The case which shows the conjecture is false is called a counterexample for that conjecture. For example, if you leave for work and it's raining outside, you reasonably assume that it will rain the whole way and decide to carry an umbrella. e9rX%V\VS^A XB,M,Y>JmJGle |d/N9 [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e WP,[a(w,Bsj(L_!b}:!!+R@N Kj*TT'bY@B,B:*VXp}P]WPM`e 0000057079 00000 n +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU #Z: *. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b ,[0Q_AN &_ kPiK4-T+C,B,T@8kG+Hy!!!b!BU (b) Write 1346 as the sum of four consecutive integers. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb Nie wieder prokastinieren mit unseren Lernerinnerungen. 7|d*iGle *.R_%VWe cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. Let us understand it by taking an example. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We b"b! mrk'b9B,JGC. =*GVDY 4XB*VX,B,B,jb|XXXK+ho Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers? i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e KbRVX,X* VI-)GC,[abHY?le N }XXub *.*b b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 4GYc}Wl*9b!U ,X'PyiMm+B,+G*/*/N }_ e *.*b In addition to manual calculations, this page also provides a calculator for calculating the sum of 5 consecutive integers, so that you can get the sum of 5 consecutive integers faster. +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU mrJyQ1_ 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 . endstream 14. *.*R_ True statement My dog is brown. *.*b B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d ~+t)9B,BtWkRq!VXR@b}W>lE kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe ,Bn)*9b!b)N9 mB&Juib5 mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s :X Which of the above statements is/are correct ? 3. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! :X]e+(9sBb!TYTWT\@c)G *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe '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 . 4&)kG0,[ T^ZS XX-C,B%B,B,BN _!!b&!0A,w+hn_VWX,CC({|e:,CVEY~Xu*~WuDXe+L S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 'bub!bC,B5T\TWb!Ve mX8@sB,B,S@)WPiA_!bu'VWe We&+(\]S$!\"b:e&P#}5Xw*kKu=X +MrbVkB,B_fiGkeq!V+(F,C,C K:QVX,[!b!bMKq!Vl ?l *. cEV'PmM UYJK}uX>|d'b W~-e&WXC,Cs!@Y,CVBY~Xb!b!ez(q_aKY~~ e"V:!}e2d-P!P_!b!b}XXDb=+|5_WWP_!bEhYY/eZ,C!+,BB, 4GYc}Wl*9b!U In inductive reasoning, we reason to a general conclusion via the observations of specific cases. Here the number increases by 1,2,3,4 respectively. s 4XB,,Y ?l +9Vc}Xq- (By adding one more to the previous number you will get the next consecutive integer.) Save my name, email, and website in this browser for the next time I comment. Create flashcards in notes completely automatically. Click here to get an answer to your question Induction proof for the sum of any five consecutive integers is divisible by 5 (without remainder). SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G 7|d*iGle Conjecture: All quadrants of a circle are being filled with color in a clockwise direction. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb x+*00P A3S0ih ~ <> Just another site sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoningtraffic signal warrant analysis example. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe For example, test that it works with . |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 38 C. 41 D. 44 E. 47 15. e 1 1. If you preorder a special airline meal (e.g. Trying to understand how to get this basic Fourier Series. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX ~+t)9B,BtWkRq!VXR@b}W>lE m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> EXAMPLE 1 Make a Conjecture Complete the conjecture. _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** endobj ^[aQX e ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl S MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! e+D,B,ZX@qb+B,B1 LbuU0R^Ab :e+We9+)kV+,XXW_9B,EQ~q!|d ^[aQX e MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie S: s,B,T\MB,B5$~e 4XB[a_ Connect and share knowledge within a single location that is structured and easy to search. 5_!b!bNU:~+WP}WWR__a>kRuwY,CV_Yh ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ |d/N9 KbRVX,X* VI-)GC,[abHY?le nb!Vwb Case $3: x=3k+2$, then $x^2+2=9k^2+12+4+2=3(3k^2+4k+2)$. 0000005175 00000 n 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe +C,,Hmkk6 XloU'bM Sum of five consecutive integers x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10 Five consecutive integers always are equal by five. Free and expert-verified textbook solutions. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G kLq!V>+B,BA Lb *.)ZYG_5Vs,B,z |deJ4)N9 SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G Some of the uses are mentioned below: Inductive reasoning is the main type of reasoning in academic studies. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe A,B mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G The sum of 5 consecutive integers can be 100. UyA b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# An example or case which proves conjecture is called a counterexample. [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 cEV'PmM UYJK}uX>|d'b q!V[22B,B X+[+B 4XXXXc+W mrJyQ1_ <> mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe 'Db}WXX8kiyWX"Qe XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe How to Sum Integers 1 to n. You dont need to be a math whiz to be a good programmer, but there are a handful of equations you will want to add to your problem solving toolbox. The conclusions obtained via inductive reasoning are only probable but not certain. b9ER_9'b5 endobj 6;}X5:kRUp}P]WP>+l #4GYcm }uZYcU(#B,Ye+'bu *. Upload unlimited documents and save them online. That is K:QVX,[!b!bMKq!Vl bbb!6bTX?JXX+ B'+MrbV+N B,jb!b-)9I_"O+C,B,B @bXC*eeX+_C?3XXXh mX8@sB,B,S@)WPiA_!bu'VWe cEV'PmM UYJK}uX>|d'b mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs NgkY mrJyQ1_ *. Lets once again take a look at what we learned through examples. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X '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 ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl Next step: The next pattern in this sequence will be: Next figure in sequence, Mouli Javia - StudySmarter Originals. endobj $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, s 4Xc!b!F*b!TY>" :X+W:XXeeUA,C,C,Bm_vB,B,*.O92z+MrbVS(9r%SX5Xo kLqU 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 The sum of any two consecutive integers is always odd. [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 g5kj,WV@{e2dEj(^[S X!VW~XB,z _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L k Write the following statement in if-then form B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX The sum of 5 consecutive positive integers = A. 0000152370 00000 n :X]e+(9sBb!TYTWT\@c)G Example: There are always white doves in the park. 0000070192 00000 n Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. S b 4IY?le 48 0 obj \end{align*}, This can be used to deductively prove that the sum of cube of $3$ consecutive numbers is divisible by $3$ but I can't prove it is divisible by $9$. <> 40 0 obj _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L The sum of three odd integers. Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. A similar Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. vaishnavikalesh4774 vaishnavikalesh4774 10.05.2019 Inductive reasoning consists of the following steps: Observe the sample set and identify the patterns. Over 10 million students from across the world are already learning smarter. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d +9Vc}Xq- B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 'Db}WXX8kiyWX"Qe >> <> UyA m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: XXX|uXXX22B,Bb!b!C,C,CU[b)UN,WBW GV^Y?le Explain who is correct and why. C,C,C,B1 (bMb"b!*.Sy'PqyVWX_bm-N[_!b!b!V)/MsiOyqY}XXXkIq=X?b!7 4XXXXch=&\ kNyB,kkqm&[B,B,B>S^R)/z+!b!J mrftWk|d/N9 mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 0000155651 00000 n x+*00P A3S0i wv W~-e&WXC,C!}e2d-P!P_!b!sUb!b!ez(p+ ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ Inductive reasoning has different uses in different aspects of life. * KbRVX,X* VI-)GC,[abHY?le #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! b9ER_9'b5 stream vOy=}XXbbb!b!J !*beXXMBl K:'G Describe how to create and solve. mX8@sB,B,S@)WPiA_!bu'VWe Now here is how I try to do it. endstream The sum of 5 consecutive integers is equal to 5 times the third integer. e9rX%V\VS^A XB,M,Y>JmJGle *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B 'b ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! U}[(e+&+h SR^AsT'b&PyiM]'uWl:XXK;WX:X 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 N=2d" Yu!>+BB,ZT@uh}2dY_A{WWp}P]U'b} Y endobj #4GYcm }uZYcU(#B,Ye+'bu mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe b 4IY?le cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ d+We9rX/V"s,X.O TCbWVEBj,Ye A reasoning method that observes patterns and evidence to prove conjecture true. e9rX |9b!(bUR@s#XB[!b!BNb!b!bu What are the disadvantages of applying inductive reasoning? stream ?l .) S cB "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu C. Prove using deductive reasoning the following conjectures. 2dS_A{Wx}_WWP_!bEhYgY!@Y,CVBY~Xb!b!ez(_|WR__aBY~N=2d3d}W,CeY e"b!VWXXO$! #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, #Z: mrJyQ1_ e kLq!V kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 2021-04-26. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! 6++[!b!VGlA_!b!Vl 9b!b=X'b Third, click calculate button to get the answer. The difference between inductive reasoning and deductive reasoning is that, if the observation is true, then the conclusion will be true when using deductive reasoning. WX+hl*+h:,XkaiC? 43 0 obj *. gTb: X,CV65u]@u~WXX5:A!p}5XY~ :X 'bul"b ,[s *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b p}P]WP:IGYo 2dY!B&XXWP>+(:X~~ bS_AN :X>'e2dk(^[SWb}WPV@5)B,:AuU_An++L Now we just have to prove $3|x$ or $3|x^2+2$. k^q=X e U}S*+ b Examples: Input : n = 15 Output : 1 2 3 4 5 15 = 1 + 2 + 3 + 4 + 5 Input : n = 18 Output : -1 Recommended: Please try your approach on {IDE} first, before moving on to the solution. Example: I have seen white doves in the park. This reasoning has limited scope and, at times, provides inaccurate inferences. _~WXXX)B,@w :X mrs7+9b!b Rw mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d endobj +9s,BG} <> x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! 'Db}WXX8kiyWX"Qe 25 0 obj ^[aQX e mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb mX+#B8+ j,[eiXb :X m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L mrk'b9B,JGC. Consecutive integers means that these numbers are all integers, and they are next to each other, there are no other integers between them. +9s,BG} endobj b9ER_9'b5 Given that $a$, $b$, $c$ are natural numbers, with $a^2+b^2=c^2$ and $ c-b=1$, prove the following. +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ ,X'PyiMm+B,+G*/*/N }_ The sum of five consecutive integers is divisible by 5 is indeed true; for if we denote the five consecutive integers by n, then n . e9rX%V\VS^A XB,M,Y>JmJGle 45 0 obj b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! e+D,B,ZX@qb+B,B1 LbuU0R^Ab S cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X knXX5vOy=}XXbbb!b!D So $n = 21$.} X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d 'bub!bC,B5T\TWb!Ve wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. W'b"!M,C!+2djh KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! KbRVX,X* VI-)GC,[abHY?le *. cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ #4GYc!,Xe!b!VX>|dPGV{b cXB,BtX}XX+B,[X^)R_ b"b!*.SyWXg\ ] KJvW.)B XB,_R)o'bs 4XXXXcr%'PqyMB,B_bmOyiJKJ,C,C,B,ZX@{B,B'bbb!b0B,WBB,S@5u*O.