English Title

The summation of an innumerable progression

Authors

Leonhard Euler

Enestrom Number

20

Fuss Index

173

Original Language

Latin

English Summaries

This paper concerns the sum of reciprocal squares, which equals π2/6. Euler does not yet have the tools to find this value directly, but instead approximates it as 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Then Euler brings in the harmonic series: letting f(x) denote the xth partial sum of the harmonic series, he approximates it as an integral and defines his constant γ as the limit of f(x) – log(x).

Published as

Journal article

Published Date

1738

Written Date

1731

Content Summary

This paper concerns the sum of reciprocal squares, which equals π2/6. Euler does not yet have the tools to find this value directly, but instead approximates it as 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Then Euler brings in the harmonic series: letting f(x) denote the xth partial sum of the harmonic series, he approximates it as an integral and defines his constant γ as the limit of f(x) – log(x).

Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 91-105.

Opera Omnia Citation

Series 1, Volume 14, pp.25-41.

Record Created

2018-09-25

Included in

Mathematics Commons

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