Hello, fair_lady!

Prove that the sum of consecutive odd numbers is always the difference of two sqaures. Here's a hint . . . maybe you can exploit it.

Fact: Consecutive odd numbers are the differences of consecutive squares. Code:

0² 1² 2² 3² 4² 5² 6² 7² 8²
0 1 4 9 16 25 36 49 64
\ / \ / \ / \ / \ / \ / \ / \ /
1 3 5 7 9 11 13 15

So that a set of consecutive odd numbers, say, 7 + 9 + 11 + 13,

. . will come from this arrangement: Code:

0² 1² 2² 3² 4² 5² 6² 7² 8²
0 1 4 9 16 25 36 49 64
\ /
7 + 9 + 11 + 13

So that (7 + 9 + 11 + 13) is the difference of 7² and 3².

Now if we can express all that *in general*, we'd have our proof.

But I haven't done it yet . . . maybe you'll have better luck.