#### English Title

The summation of an innumerable progression

#### Enestrom Number

20

#### Fuss Index

173

#### Original Language

Latin

#### English Summaries

This paper concerns the sum of reciprocal squares, which equals π^{2}/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 *x*th 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 Ï^{2}/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 *x*th partial sum of the harmonic series, he approximates it as an integral and defines his constant Î³ 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