Problem:
Read
http://ptri1.tripod.com/And then prove the sum of squares formula, i.e.
1 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6
by use of the Hockey Stick Identity (an important combinatorics identity which is explained in that link).
EDIT: Deriving the sum of squares formula by finite differences takes awhile and is thus annoying. For instance, to do it by finite differences you have to first make a large-enough table, then you have to establish the order of the polynomial, and then you have to solve a 3x4 augmented matrix. But deriving it with the Hockey Stick Identity only takes like a minute (once you know how to do it). So knowing how to derive it with the Hockey Stick identity allows you to derive it quickly
