mathschallenge.net

Problem

It can be seen that $6^2 - 5^2 + 4^2 - 3^2 + 2^2 - 1^2 = 21 = T_6$, the sixth triangle number.

Prove that the $n$th triangle number, $T_n = n^2 - (n - 1)^2 + (n - 2)^2 - ... 1^2$.