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

well, i can see it visually.

start with 1 marble:
1
one marble = 1 squared

then add 3 marbles:
13
33
four marbles = 2 squared

add 5 marbles:
135
335
555

continuing on:
1357
3357
5557
7777

as we see, each odd number being added is basically adding another row and column to the square.

yeah, this isn't a very mathematical proof. oh well.

Posted by Happy on 2002-08-08 08:42:19