OFFSET
0,1
COMMENTS
The divergent series Sum_{n>=1} sin(n) sums to this value if interpreted as a geometric series; that is, Sum_{n>=1} sin(n) = Im(Sum_{n>=1} e^(ni)) = Im(-e^i/(e^i-1)) = 1/(2*tan(1/2)). If x_m = Sum_{0<n<m} sin(n), then (max(x_1, x_2, ...) + min(x_1, x_2, ...))/2 tends to this number. Given by the series 1+Sum_{n>=1} (-1)^n B_(2n)/(2n)!. Corresponding value for cos is -1/2.
FORMULA
Equals Sum_{k>=0} (-1)^k * bernoulli(2*k)/(2*k)! = Sum_{k>=0} (-1)^k * A027641(2*k)/(A027642(2*k)*(2*k)!). - Amiram Eldar, Jul 22 2020
EXAMPLE
0.915243860856225...
MATHEMATICA
RealDigits[N[1/(2 Tan[1/2]), 101]]
PROG
(PARI) 1/(2*tan(1/2)) \\ Michel Marcus, Jul 22 2020
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Fredrik Johansson, Aug 20 2006
STATUS
approved