OFFSET
0,1
COMMENTS
As v(n) = log(n*sin(1/n)) ~ -1/(6*n^2) when n -> oo, this series is convergent (zeta(2)/6 ~ 0.2741556778...).
FORMULA
Equals Sum_{n>=1} log(n*sin(1/n)).
Equals log(A295219).
From Amiram Eldar, Jul 30 2023: (Start)
Equals Sum_{k>=1} 2^(2*k-1)*(-1)^k*B(2*k)*zeta(2*k)/(k*(2*k)!), where B(k) is the k-th Bernoulli number.
Equals -Sum_{k>=1} zeta(2*k)^2/(k*Pi^(2*k)). (End)
EXAMPLE
-0.28055633622915507960203968093919836217450282945971...
MAPLE
evalf(sum(log(n*sin(1/n)), n=1..infinity), 50);
PROG
(PARI) sumpos(n=1, log(n*sin(1/n))) \\ Michel Marcus, Jul 20 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Jul 20 2020
EXTENSIONS
More terms from Jinyuan Wang, Jul 21 2020
STATUS
approved