A099872 Decimal expansion of Sum_{n>=1} ((-1)^(n+1))/(n^log(n)).

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

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

Keywords

• cons
• easy
• nonn

Examples

			0.58330232817831614516388747578415335926010055878702864402371232644...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Magma

SetDefaultRealField(RealField(100)); [(&+[(-1)^(k+1)/k^Log(k): k in [1..1000]])]; // G. C. Greubel, Nov 20 2018

Maple

evalf(Sum(((-1)^(n+1))/(n^log(n)), n=1..infinity), 120); # Vaclav Kotesovec, Mar 01 2016

Mathematica

RealDigits[ NSum[ -(-1)^n/n^Log[n], {n, Infinity}, AccuracyGoal -> 2^10, Compiled -> True, WorkingPrecision -> 2^10, NSumExtraTerms -> 256, NSumTerms -> 512], 10, 111][[1]] (* Robert G. Wilson v, Dec 21 2004 *)

PARI

sumalt(n=1,((-1)^(n+1))/(n^log(n)))

Sage

numerical_approx(sum((-1)^(k+1)/k^log(k) for k in [1..1000]), digits=100)