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Odd Sum (
Posted on 20020808
)
Prove that the sum of consecutive odd numbers beginning at 1 (
eg 1, 3, 5, ..
) always adds up to a perfect square
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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 = (10) + (41) + (94) + ... + ((N+1)^2  N^2) = (11) + (44) + ... + (N^2  N^2) + (N+1)^2 = (N+1)^2.
Posted by
Richard
on 20040404 18:12:59
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