A357054 Decimal expansion of Sum_{k>=1} (-1)^(k+1)*k/Fibonacci(2*k).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Daniel Duverney and Iekata Shiokawa, On series involving Fibonacci and Lucas numbers I, AIP Conference Proceedings, Vol. 976, No. 1. American Institute of Physics, 2008, pp. 62-76.

Derek Jennings, On reciprocals of Fibonacci and Lucas numbers, Fibonacci Quarterly, Vol. 32, No. 1 (1994), pp. 18-21.

Formula

Equals Sum_{k>=1} (-1)^(k+1)*k/A001906(k).

Equals (1/sqrt(5)) * Sum_{k>=1} 1/Fibonacci(2*k-1)^2 (Jennings, 1994).

Example

0.58000473950777068006747098189552280269850126096461...

Mathematica

RealDigits[Sum[(-1)^(k+1)*k/Fibonacci[2*k], {k, 1, 300}], 10, 100][[1]]

Prog

(PARI) sumalt(k=1, (-1)^(k+1)*k/fibonacci(2*k)) \\ Michel Marcus, Sep 10 2022

Crossrefs

Cf. A000045, A001519, A001906, A081068, A357053.

Cf. A079586, A153386, A153387, A158933, A265288.

Sequence in context: A257774 A281386 A090817 * A198875 A249403 A201756

Adjacent sequences: A357051 A357052 A357053 * A357055 A357056 A357057

Keyword

nonn,cons

Author

Amiram Eldar, Sep 10 2022

Status

approved