A348763 Decimal expansion of Sum_{n>=1} ((-1)^(n+1)*n)/(n+1)^2.
1, 2, 9, 3, 1, 9, 8, 5, 2, 8, 6, 4, 1, 6, 7, 9, 0, 8, 8, 1, 8, 9, 7, 5, 4, 6, 1, 8, 6, 4, 8, 3, 6, 0, 2, 6, 5, 3, 3, 9, 7, 4, 8, 1, 6, 2, 4, 3, 1, 4, 3, 9, 6, 4, 7, 4, 7, 0, 9, 9, 1, 0, 5, 1, 9, 1, 6, 1, 0, 1, 1, 3, 2, 3, 1, 9, 0, 5, 7, 2, 1, 3, 1, 0, 9
Offset: 0
Examples
0.12931985286416790881897546186483602653397481624314396474709910519161011...
Links
- Eric Weisstein's World of Mathematics, Dilogarithm
- Index entries for zeta function.
Programs
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Mathematica
RealDigits[Pi^2/12 - Log[2], 10, 100][[1]] (* Amiram Eldar, Nov 30 2021 *)
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PARI
-sumalt(n=1, (-1)^n*n/(n+1)^2) \\ Charles R Greathouse IV, Nov 01 2021
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PARI
Pi^2/12-log(2) \\ Charles R Greathouse IV, Nov 01 2021
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Python
from scipy.special import zeta from math import log int(''.join(n for n in list(str(zeta(2)/2-log(2)))[2:-2])) -
Python
int(str(sum((-1)**(n+1)*n/(n+1)**2 for n in range(1,5000000)))[2:-2])
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SageMath
(pi^2/12-log(2)).n(digits=100)
Formula
Equals Pi^2/12-log(2).
Equals Sum_{k>=2} (zeta(k)-zeta(k+1))/2^k. - Amiram Eldar, Mar 20 2022
Equals Integral_{x >= 0} x/(1 + exp(x))^2 dx = (1/2) * Integral_{x >= 0} x*(x - 2)*exp(x)/(1 + exp(x))^2 dx . - Peter Bala, Apr 26 2025