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A374062
Decimal expansion of Sum_{n>=1} [sqrt(n^3+1)-sqrt(n^3-1)].
1
3, 0, 2, 7, 3, 2, 2, 0, 3, 6, 6, 2, 6, 2, 3, 9, 5, 2, 8, 8, 8, 7, 9, 2, 0, 9, 0, 5, 6, 7, 3, 2, 3, 1, 3, 2, 3, 2, 6, 9, 2, 1, 1, 8, 4, 1, 7, 4, 5, 8, 2, 1, 2, 7, 1, 8, 5, 5, 6, 7, 9, 0, 1, 6, 6, 5, 9, 4, 7, 8, 1, 9, 8, 1, 2, 1, 9, 4, 9, 9, 3, 8, 8, 3, 4
OFFSET
1,1
LINKS
Math StackExchange, Convergence of..., Jul 21 2020.
FORMULA
Sum_{n>=1} [sqrt(n^s+1)-sqrt(n^s-1)] = sqrt(2)+2*Sum_{j>=0} binomial(1/2,2*j+1) [zeta(s/2+2*j*s)-1], s>2.
EXAMPLE
3.027322036626239528887920...
PROG
(PARI) sqrt(2) + 2 * sumpos(j = 0, binomial(1/2, 2*j+1) * (zeta(6*j + 3/2) - 1)) \\ Amiram Eldar, Aug 20 2024
CROSSREFS
Cf. A374063 (s=4).
Sequence in context: A209129 A368479 A282694 * A011075 A248820 A085550
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 27 2024
STATUS
approved