A234014 Decimal expansion of Sum_{x>=2} 1/((x - 1) sqrt(x)) = Sum_{k>=1} (zeta(k+1/2) - 1).
2, 1, 8, 4, 0, 0, 9, 4, 7, 0, 2, 6, 7, 8, 5, 1, 9, 5, 2, 8, 9, 4, 7, 3, 4, 1, 5, 7, 8, 5, 2, 9, 4, 9, 0, 7, 0, 4, 4, 3, 9, 0, 8, 4, 0, 6, 2, 6, 3, 2, 2, 9, 4, 2, 0, 2, 0, 0, 2, 5, 1, 2, 0, 7, 9, 2, 8, 3, 5, 4, 9, 0, 3, 1, 1, 2, 7, 4, 0, 2, 9, 5, 3, 9, 0, 6, 9, 7, 4, 1, 8, 4, 6, 1, 3, 4, 1, 6, 1, 9, 7, 2, 3, 0, 7
Offset: 1
Examples
2.184009470267851952894734157852949070443908406263229420200251207928354...
Links
- David Brink, The Spiral of Theodorus and Sums of Zeta-values at the Half-Integers, The American Mathematical Monthly, Vol 119, No. 9 (November 2012), page 785.
Programs
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Mathematica
RealDigits[ Sum[ Zeta[k + 1/2] - 1, {k, 1, 355}], 10, 111][[1]] -
PARI
sum(k=1,340,zeta(k+1/2)-1)