OFFSET
0,2
LINKS
Martin Janecke, Edle Reihe
FORMULA
lim_{n->infinity} (1/[1;1,...] + 1/[2;2,...] + 1/[3;3,...] + ... + 1/[n;n,...] - log(n)).
lim_{n->infinity} (sum_{k=1...n} (2/(k + sqrt(k^2 + 4))) - log(n)).
EXAMPLE
0.0416662....
MATHEMATICA
digits = 10; dn = 1000000; Clear[f]; f[n_] := NSum[2/(k + Sqrt[k^2+4]) - 1/k, {k, 1, Infinity}, NSumTerms -> 200000, WorkingPrecision -> digits+10, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 20}}] + EulerGamma // RealDigits[#, 10, digits+2]& // First; f[dn]; f[n = 2*dn]; While[f[n] != f[n-dn], n = n+dn]; Prepend[ f[n][[1 ;; digits]], 0] (* Jean-François Alcover, Feb 25 2013 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Martin Janecke, Jan 26 2012
EXTENSIONS
More terms from Jean-François Alcover, Feb 25 2013
More terms from Jon E. Schoenfield, Jan 05 2014
STATUS
approved