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

(In reply to What, me worry? by Steve Herman)

Some of them do look a bit complicated.

To get from the nth square to the n+1th square we need to add n units on each of two adjacent sides, plus 1 in the corner; i.e. 2n+1.

n^2+2n+1=(n+1)^2.

No need to sum series or anything like that.

Posted by broll on 2015-04-06 03:56:52