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August 18th, 2015, 10:15 AM   #1
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Unhappy 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
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Last edited by med1student; August 18th, 2015 at 10:28 AM.
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August 18th, 2015, 12:40 PM   #2
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$\displaystyle =\sum_{m=1}^3\sum_{k=0}^2((k+2+m)+(k+3+m)+(k+4+m)) =$,
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
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August 18th, 2015, 03:16 PM   #3
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Wait what induction?
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August 18th, 2015, 05:13 PM   #4
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$\displaystyle \sum_{i=2}^4\sum_{m=1}^3\sum_{k=0}^2k + \sum_{m=1}^3\sum_{k=0}^2\sum_{i=2}^4i + \sum_{k=0}^2\sum_{i=2}^4\sum_{m=1}^3m = 9(0 + 1 + 2) + 9(2 + 3 + 4) + 9(1 + 2 + 3) = 162$
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August 19th, 2015, 06:59 AM   #5
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Quote:
Originally Posted by neelmodi View Post
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.
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August 19th, 2015, 08:11 AM   #6
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I always though that induction is a method of mathematical proof, so... I think the problem is not related to induction.
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