|
%I #38 Oct 25 2015 10:57:10
%S 2,7,1,9,7,7,1,3,3,2,4,8,6,3,5,5,1,0,6,3,4,4,0,2,2,6,0,5,8,3,7,8,5,4,
%T 3,5,9,3,7,7,8,1,0,2,6,7,4,6,3,9,3,6,9,7,2,9,9,1,1,0,7,6,3,0,6,5,0,2,
%U 6,0,6,3,7,9,9,3,3,6,6,7,6,7,2,3,0,8,3,2,4,3,2,9,1,3,5,8,0,1,7,4,5,9,4,0,9
%N 2 * Sum_{n>=3} 1/Fibonacci(n).
%C Also the decimal expansion of the sum of the reciprocals of averages of adjacent pairs of Fibonacci numbers: Sum_{n>=1} 2/(A000045(n) + A000045(n+1)).
%H Matematico Fresnillense, <a href="http://matematicofresnillense.blogspot.mx/2015/07/constante-entre-numeros-fibonacci.html">Constante suma inversos de promedios de Números Fibonacci</a>
%F Equals 2*A079586 - 4. - _Michel Marcus_, Aug 18 2015
%e 2.719771332486355106344022605837854359377810267463936972991107630650260637993...
%t adjFibAvRecipSum = Table[Sum[2/(Fibonacci[n] + Fibonacci[n + 1]), {n, 1000}]]; N[adjFibAvRecipSum, 20]
%t s = 0; k = 1; a = 2; b = 3; While[k < 525, s = N[s + 1/a, 128]; k++; {a, b} = {b, a + b}]; RealDigits[ 2s, 10, 111][[1]] (* _Robert G. Wilson v_, Aug 21 2015 *)
%o (PARI) suminf(n=3,2/fibonacci(n)) \\ _Charles R Greathouse IV_, Aug 20 2015
%Y Cf. A000045, A079586.
%K nonn,cons
%O 1,1
%A _José de Jesús Camacho Medina_, Aug 17 2015
|
