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Topic: Here's a little challenge for you guys.
Replies: 2   Last Post: Oct 12, 2013 6:39 PM

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Posts: 132
Registered: 11/27/12
Re: Here's a little challenge for you guys.
Posted: Oct 12, 2013 6:39 PM
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That's a pretty standard College Freshman algebra problem. "The sum of odd integers, from 1 to 2n- 1, is equal to n^2". It can be proved by induction on n.

When n= 1, this is just 1= 2(1)-1 and the sum is 1= 1^2.

Supose it is true for some specific integer, k. That is, that 1+ 3+ 5+ ...+ (2k- 1)= k^2.

Then the sum of integers for the next integer, k+ 1, is 1+ 2+ 5+ ...+ (2k- 1)+ (2(k+1)- 1)= [1+ 2+ 5+ ...+ (2k- 1)]+ (2k+1)= k^2+ 2k+ 1= (k+ 1)^2.

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