Prove that the sum of consecutive odd numbers beginning at 1 (eg 1, 3, 5, ..) always adds up to a perfect square

Note that (n+1)^2 - n^2 = 2n+1. Hence 1 + 3 + ... + 2N+1 = (1-0) + (4-1) + (9-4) + ... + ((N+1)^2 - N^2) = (1-1) + (4-4) + ... + (N^2 - N^2) + (N+1)^2 = (N+1)^2.

Posted by Richard on 2004-04-04 18:12:59