OFFSET
-6,1
LINKS
Robert G. Wilson v, Table of n, a(n) for n = -6..10000
Brother Alfred Brousseau, Summation of Infinite Fibonacci Series, The Fibonacci Quarterly, Vol. 7, No. 2 (1969), pp. 143-168. See (23) p. 167.
Stanley Rabinowitz, Algorithmic summation of reciprocals of products of Fibonacci numbers, The Fibonacci Quarterly, Vol. 37 (1999), pp. 122-127, alternative link. See (29) p. 127 or p. 7.
FORMULA
Equals to (319/16380) * (Sum_{k>=1} 1/F(k) - 46816051/13933920), where F(k) is the k-th Fibonacci number.
EXAMPLE
4.57152276206481837259844557288951854911372601255793... * 10^(-7).
MATHEMATICA
digits = 100; f[n_] := Product[Fibonacci[k], {k, n, n+8}]; NSum[1/f[n], {n, 1, Infinity}, WorkingPrecision -> digits, NSumTerms -> digits] // RealDigits[#, 10, digits] & // First (* after Jean-François Alcover at A079586 *)
RealDigits[ Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k + 8}], 128], {k, 59}], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2019 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 24 2018
STATUS
approved