A217706 Decimal expansion of -Sum( n>=2, (-1)^n*log(1 - 1/(n*(n-1))) ).

5, 6, 6, 5, 5, 3, 1, 0, 9, 7, 5, 8, 6, 0, 3, 0, 3, 0, 4, 5, 3, 1, 3, 9, 4, 1, 0, 1, 5, 2, 0, 5, 3, 7, 9, 2, 7, 9, 7, 2, 5, 4, 6, 2, 7, 2, 3, 9, 9, 7, 0, 9, 6, 5, 5, 2, 1, 7, 0, 4, 5, 5, 8, 4, 1, 0, 4, 5, 1, 0, 0, 7, 6, 3, 0, 8, 9, 7, 9, 6, 5, 0, 7, 2, 8, 5, 9, 2, 8, 6, 0, 8, 7, 5, 7, 1, 6, 9, 4, 6, 9, 8, 7, 1, 0

Offset

0,1

Links

Table of n, a(n) for n=0..104.

StackExchange, A challenging alternating infinite series involving ln

Example

The sum (without the minus sign) is negative: -0.56655310975860303045313941015205379279725462723997096552170...

Mathematica

2*ArcCsch[2] + Log[2] + LogGamma[(3 - GoldenRatio)/2] + LogGamma[GoldenRatio/2] - LogGamma[1 - GoldenRatio/2] - LogGamma[(GoldenRatio - 1)/2] // RealDigits[#, 10, 100]& // First

Crossrefs

Sequence in context: A153415 A154010 A258750 * A064864 A004553 A074826

Adjacent sequences: A217703 A217704 A217705 * A217707 A217708 A217709

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 20 2013

Extensions

Offset corrected by and more terms from Rick L. Shepherd, Jan 13 2014

Status

approved