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Decimal expansion of Sum_{k>=1} 1/(k^(1/5)*(1+k)).
2

%I #10 Jun 09 2024 23:57:22

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

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

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

%N Decimal expansion of Sum_{k>=1} 1/(k^(1/5)*(1+k)).

%F Equals Sum_{i>=0} (-1)^i*zeta(6/5+i).

%e 4.71961753816261448360578272400...

%o (PARI) sumalt(i=0,(-1)^i*zeta(6/5+i)) \\ _Hugo Pfoertner_, Mar 19 2024

%Y Cf. A226317 (for k^1/2), A371331 (k^1/3), A371332 (k^1/4).

%K nonn,cons

%O 1,1

%A _R. J. Mathar_, Mar 19 2024