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Simple Proofs for \(\sum_{k=1}^{\infty} \frac{1}{k^2} = \frac{π^2}{6}\) and \(\sin x = x \prod_{k=1}^{\infty}(1 - \frac{x^2}{k^2\pi^2})\)

by R. A. Kortram

This article originally appeared in:
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 sine function, are proved again.

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