English Title
Finding the sum of any series from a given general term
Enestrom Number
47
Fuss Index
172
Original Language
Latin
Content Summary
Euler continues with the methods of E25 to attack ζ(2) for a second time. He starts with a Taylor series, builds a "Bernoulli polynomial" and uses it to evaluate 0n + 1n + 2n + 3n + ... + (x-1)n, (x = 1, 2, 3, ...) and gets the relationship (B+1)n+1 – Bn+1 = 0 for Bernoulli numbers. He gets an infinite series approximation for the nth partial sum of the harmonic series.
Published as
Journal article
Published Date
1741
Written Date
1735
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 9-22.
Opera Omnia Citation
Series 1, Volume 14, pp.108-123.
Record Created
2018-09-25
