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 A087495 Decimal expansion of Khinchin mean K_{-5}. 10

%I

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

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

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

%N Decimal expansion of Khinchin mean K_{-5}.

%C Khinchin's constant is K_0.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KhinchinsConstant.html">Khinchin's Constant</a>

%e 1.18900392...

%t m = 5; digits = 100; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^m*Log[2])); s[n_] = Series[f[n], {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[f[n], {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n], {n, exactEnd + 1, Infinity}] // N[#, digits]&; (exactSum + extraSum)^(-1/m) // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 14 2013 *)

%Y Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.

%K nonn,cons

%O 1,3

%A _Eric W. Weisstein_, Sep 09 2003

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Last modified March 26 00:37 EDT 2019. Contains 321479 sequences. (Running on oeis4.)