My Math Forum Induction

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August 18th, 2015, 09:15 AM   #1
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Joined: Aug 2015
From: Podgorica

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Induction

Hello, can you help me solve or at least explain this problem? Yesterday I have started practicing Inductions,sequences and series but today it seems that I got stuck at this problem.
Result:
A)124
B)136
C)144
D)158
E)162
Attached Images
 mk.PNG (5.1 KB, 7 views)

Last edited by med1student; August 18th, 2015 at 09:28 AM.

 August 18th, 2015, 11:40 AM #2 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 $\displaystyle =\sum_{m=1}^3\sum_{k=0}^2((k+2+m)+(k+3+m)+(k+4+m)) =$, collect like terms, $\displaystyle =\sum_{m=1}^3\sum_{k=0}^2(3k+3m+9)=$ $\displaystyle =\sum_{m=1}^3((3m+9)+(3+3m+9)+(6+3m+9))=$, collect like terms, ... =162 Thanks from med1student
 August 18th, 2015, 02:16 PM #3 Senior Member   Joined: Aug 2014 From: United States Posts: 136 Thanks: 21 Math Focus: Learning Wait what induction?
 August 18th, 2015, 04:13 PM #4 Global Moderator   Joined: Dec 2006 Posts: 17,482 Thanks: 1314 $\displaystyle \sum_{i=2}^4\sum_{m=1}^3\sum_{k=0}^2k + \sum_{m=1}^3\sum_{k=0}^2\sum_{i=2}^4i + \sum_{k=0}^2\sum_{i=2}^4\sum_{m=1}^3m = 9(0 + 1 + 2) + 9(2 + 3 + 4) + 9(1 + 2 + 3) = 162$ Thanks from med1student and Yash Malik
August 19th, 2015, 05:59 AM   #5
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From: Alabama

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Quote:
 Originally Posted by neelmodi Wait what induction?
Are you clear on what "induction" is? It is a technique for proving that a given statement is true for all positive integers.

Since this problem allows m and k to take on only a finite number of values, induction is not appropriate.

In fact, since that 'finite number of values' is very small (1, 2, and 3 for m, 0, 1, and 2 for k) there is no reason at all not to right out all the terms as skaa and skipjack did.

 August 19th, 2015, 07:11 AM #6 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 I always though that induction is a method of mathematical proof, so... I think the problem is not related to induction. Thanks from med1student

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