Josef Hofbauer (2000):

A simple proof of 1 + 1/22 + 1/32 + ... = PI2/6 and related identities

American Mathematical Monthly 109 (February 2002), 196-200.

Abstract.
I present short and elementary proofs of Euler's series, the partial fraction series for sin-2 x, and the Gregory-Leibniz series.

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