grei
Posts:
132
Registered:
11/27/12


Re: Here's a little challenge for you guys.
Posted:
Oct 12, 2013 6:39 PM


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.

