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Alternating Sign Square Sum

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, $T_n = n^2 - (n - 1)^2 + (n - 2)^2 - ... 1^2$.

Problem ID: 262 (29 Jan 2006)     Difficulty: 3 Star

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