Démonstration de la somme de cette suite 1 + 1/4 + 1/9 + 1/16 + ...

English Title

Demonstration of the sum of the series 1 + 1/4 + 1/9 + 1/16 + ...

Authors

Leonhard Euler

Enestrom Number

63

Original Language

French

Archive Notes

The Euler Archive's version of this article is a reprinting from Paul Stäckel's 1907 article, "Eine vergessene Abhandlung Leonhard Eulers über die Summe der reziproken Quadrate der natürlichen Zahlen," Bibliotheca mathematica 3 pp. 37-60.

The original 1743 article can be found online at Google Books.

Content Summary

The answer hasn't changed; it's still π²/6. He does the sum of the odd square reciprocals using an arcsine integral, and considers the differential equation (1−x²)y'' − xy' − 1 = 0.

Published as

Journal article

Published Date

1743

Written Date

1741

Original Source Citation

Journal litteraire d'Allemagne, de Suisse et du Nord, Volume 2, pp. 115-127.

Opera Omnia Citation

Series 1, Volume 14, pp. 177-186.

Record Created

2018-09-25