A308915 Decimal expansion of Sum_{n>=1} 1/(log(n)^log(n)).

6, 7, 1, 6, 9, 7, 0, 6, 1, 2, 9, 9, 0, 8, 9, 6, 0, 8, 8, 1, 4, 4, 5, 7, 9, 9, 8, 7, 2, 3, 2, 6, 0, 8, 8, 9, 1, 4, 5, 2, 7, 7, 2, 6, 1, 6, 5, 8, 8, 4, 5, 0, 4, 5, 8, 2, 6, 7, 0, 7, 5, 9, 2, 8, 4, 0, 5, 2, 4, 0, 2, 1, 8, 0, 6, 9, 3, 2, 5, 0, 9, 4, 3, 3, 5, 1, 1, 0, 0, 1, 8, 7, 5, 7, 2, 7, 6, 4, 2

Offset: 1

Author

Bernard Schott, Jun 30 2019

Keywords

• cons
• nonn

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.

Examples

			6.71697061299089608814457...
		

References

• Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.i p. 279.

Crossrefs

Cf. A073009 (1/n^n), A099870 (1/n^log(n)), A099871 (1/log(n)^n).

Programs

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 *)

PARI

1 + sumpos(n=2, 1/(log(n)^log(n))) \\ Michel Marcus, Jun 30 2019

Formula

Equals Sum_{n>=1} 1/(log(n)^log(n)).

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