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 Algebra Pre-Algebra and Basic Algebra Math Forum

August 18th, 2015, 09:15 AM   #1
Member

Joined: Aug 2015
From: Podgorica

Posts: 61
Thanks: 0 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: 137 Thanks: 21 Math Focus: Learning Wait what induction? August 18th, 2015, 04:13 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2215 $\displaystyle \sum_{i=2}^4\sum_{m=1}^3\sum_{k=0}^2k + \sum_{m=1}^3\sum_{k=0}^2\sum_{i=2}^4i + \sum_{k=0}^2\sum_{i=2}^4\sum_{m=1}^3m = 9(0 + 1 + 2) + 9(2 + 3 + 4) + 9(1 + 2 + 3) = 162$ Thanks from med1student and Yash Malik August 19th, 2015, 05:59 AM   #5
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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 Tags induction Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cool012 Algebra 0 December 1st, 2013 05:37 AM OriaG Algebra 11 October 27th, 2012 03:55 PM restin84 Algebra 4 March 24th, 2012 06:18 PM restin84 Number Theory 2 December 31st, 1969 04:00 PM OriaG Calculus 0 December 31st, 1969 04:00 PM

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