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Decimal expansion of Sum_{n>=2} 1/log(n)^sqrt(n).
2

%I #12 Aug 06 2020 04:10:14

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

%T 7,9,0,4,1,0,0,6,7,5,5,3,1,9,7,0,6,5,5,7,3,0,7,5,7,4,9,2,5,0,6,6,0,1,

%U 8,8,2,7,3,4,5,4,1,7,1,0,1,1,2,5,2,5,1

%N Decimal expansion of Sum_{n>=2} 1/log(n)^sqrt(n).

%C The series u(n) = 1/log(n)^sqrt(n) is convergent because n^2 * u(n) -> 0 when n -> oo.

%D J.-M. Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.1.d p. 247.

%F Equals Sum_{n>=2} 1/log(n)^sqrt(n).

%e 4.372450021106629664550827989755553790410067553197...

%p evalf(sum(1/(log(n)^sqrt(n), n=2..infinity), 120);

%o (PARI) sumpos(n=2, 1/log(n)^sqrt(n)) \\ _Michel Marcus_, Aug 03 2020

%Y Cf. A099870, A099871, A308915.

%K nonn,cons

%O 1,1

%A _Bernard Schott_, Aug 02 2020

%E More terms from _Jinyuan Wang_, Aug 03 2020