login
Decimal expansion of the infinite sum 1/log(2) + 1/(log(2)*log(3)) + 1/(log(2)*log(3)*log(4)) + ...
0

%I #8 Mar 18 2013 09:35:05

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

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

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

%N Decimal expansion of the infinite sum 1/log(2) + 1/(log(2)*log(3)) + 1/(log(2)*log(3)*log(4)) + ...

%e 4.934269949...

%t digits = 100; NSum[ Product[1/Log[k], {k, 2, n}], {n, 2, Infinity}, NSumTerms -> digits+40, WorkingPrecision -> digits+10] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Mar 18 2013 *)

%K cons,nonn,easy

%O 1,1

%A _Jean-François Alcover_, Mar 18 2013