OFFSET
1,1
COMMENTS
This series is convergent because n^2 * 1/log(n)^log(n) = exp(log(n) * (2 - log(log(n)))) which -> 0 as n -> oo.
REFERENCES
Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.i p. 279.
FORMULA
Equals Sum_{n>=1} 1/(log(n)^log(n)).
EXAMPLE
6.71697061299089608814457...
MAPLE
evalf(sum(1/(log(n)^log(n)), n=1..infinity), 110);
MATHEMATICA
RealDigits[N[1 + Sum[1/Log[n]^Log[n], {n, 2, Infinity}], 100]][[1]] (* Jinyuan Wang, Jul 25 2019 *)
PROG
(PARI) 1 + sumpos(n=2, 1/(log(n)^log(n))) \\ Michel Marcus, Jun 30 2019
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Bernard Schott, Jun 30 2019
EXTENSIONS
More terms from Jon E. Schoenfield, Jun 30 2019
a(16)-a(24) from Jinyuan Wang, Jul 10 2019
More terms from Charles R Greathouse IV, Oct 21 2021
STATUS
approved