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A374063
Decimal expansion of Sum_{n>=1} [sqrt(n^4+1)-sqrt(n^4-1)].
1
2, 0, 5, 9, 2, 7, 2, 1, 6, 0, 3, 5, 2, 0, 2, 3, 8, 1, 3, 1, 9, 0, 9, 2, 1, 9, 2, 5, 1, 3, 9, 6, 1, 0, 0, 1, 0, 7, 2, 4, 4, 6, 8, 1, 8, 5, 1, 7, 4, 7, 1, 0, 6, 3, 0, 3, 5, 3, 3, 0, 2, 8, 9, 9, 1, 2, 8, 8, 0, 0, 7, 1, 0, 2, 9, 0, 7, 2, 2, 9, 8, 8, 5, 2, 8, 8, 7, 1
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
2.059272160352023813190921925139...
PROG
(PARI) sqrt(2) + 2 * sumpos(j = 0, binomial(1/2, 2*j+1) * (zeta(8*j + 2) - 1)) \\ Amiram Eldar, Aug 20 2024
CROSSREFS
Cf. A374062 (s=3).
Sequence in context: A011435 A139309 A264299 * A243445 A227569 A344786
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 27 2024
STATUS
approved