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Odd Sum (Posted on 2002-08-08) Difficulty: 2 of 5
Prove that the sum of consecutive odd numbers beginning at 1 (eg 1, 3, 5, ..) always adds up to a perfect square

See The Solution Submitted by Cheradenine    
Rating: 3.9000 (10 votes)

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Difference Method | Comment 7 of 17 |
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
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