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 A217706 Decimal expansion of -Sum( n>=2, (-1)^n*log(1 - 1/(n*(n-1))) ). 0

%I

%S 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,

%T 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,

%U 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

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

%H StackExchange, <a href="http://math.stackexchange.com/questions/69090/challenging-alternating-infinite-series-involving-ln">A challenging alternating infinite series involving ln</a>

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

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

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Mar 20 2013

%E Offset corrected by and more terms from _Rick L. Shepherd_, Jan 13 2014

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)