You are here

Simple Proofs for Two Famous Euler Identities

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 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 \(\sin x = x \prod_{k=1}^{\infty}(1 - \frac{x^2}{k^2\pi^2})\)."

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Average: 3.1 (64 votes)