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Decimal expansion of Sum_{n>=1} Zeta(2n)/n! = 2.40744...
5

%I #20 Mar 20 2017 03:40:21

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

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

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

%N Decimal expansion of Sum_{n>=1} Zeta(2n)/n! = 2.40744...

%H G. C. Greubel, <a href="/A076813/b076813.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>

%e 2.40744655479032851470948665622302272558226649037984418869339833...

%p evalf(Sum(exp(1/n^2)-1, n=1..infinity), 120); # _Vaclav Kotesovec_, Mar 04 2016

%t rd[k_] := rd[k] = RealDigits[ N[ Sum[ Zeta[2n]/n!, {n, 1, 2^k}], 105]][[1]][[1 ;; 102]]; rd[k = 4]; While[ rd[k] != rd[k-1], k++]; rd[k] (* _Jean-François Alcover_, Oct 29 2012 *)

%o (PARI) suminf(n=1, zeta(2*n)/n!) \\ _Michel Marcus_, Mar 20 2017

%K nonn,cons

%O 1,1

%A _Eric W. Weisstein_, Oct 16 2002