Simple Proofs for Two Famous Euler Identities

by R. A. Kortram

Mathematics Magazine
April, 1996

Subject classification(s): Single Variable Calculus | Series
Applicable Course(s): 4.11 Advanced Calc I, II, & Real Analysis

Two of Euler's familiar identities, the sum of reciprocals of squares of integers and the infinite product expression of the sine function, are proved again. This article originally appeared as "Simple Proofs for $$\sum_{k=1}^{\infty} \frac{1}{k^2} = \frac{π^2}{6}$$ and $$\sin x = x \prod_{k=1}^{\infty}(1 - \frac{x^2}{k^2\pi^2})$$."

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