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
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 27 2024
STATUS
approved