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Decimal expansion of Sum_{n>=2} sqrt(n)^log(n)/log(n)^sqrt(n).
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%I #13 Aug 22 2020 02:37:24

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

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

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

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

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

%D J. Moisan & A. Vernotte, Analyse, Topologie et Séries, Exercices corrigés de Mathématiques Spéciales, Ellipses, 1991, Exercice B-1 a-3 pp. 70, 87-88.

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

%e 32.219419584243365152435936117722884...

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

%o (PARI) default(realprecision, 100); sumpos(n=2, sqrt(n)^log(n)/log(n)^sqrt(n)) \\ _Michel Marcus_, Aug 10 2020

%Y Cf. A099870, A308915, A336284, A336741.

%K nonn,cons

%O 2,1

%A _Bernard Schott_, Aug 10 2020

%E a(37)-a(101) from _Robert Price_, Aug 21 2020