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A158933 Decimal expansion of sum{n>=1}((-1)^(n+1))*1/F(n) where F(n) is the n-th Fibonacci number A000045(n). 2

%I

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

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

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

%N Decimal expansion of sum{n>=1}((-1)^(n+1))*1/F(n) where F(n) is the n-th Fibonacci number A000045(n).

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">MathWorld: Reciprocal Fibonacci Constant</a>

%e .2891446485706715831123055096157291669...

%p with(combinat, fibonacci):Digits:=100:s:=0:for n from 1 to 2000 do: a1:=fibonacci(n):s:=s+evalf(1/a1)*(-1)^(n+1):od:print(s):

%t digits = 95; NSum[(-1)^(n+1)*(1/Fibonacci[n]), {n, 1, Infinity}, WorkingPrecision -> digits+1, NSumTerms -> digits] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Jan 28 2014 *)

%o (PARI) -sumalt(n=1,(-1)^n/fibonacci(n)) \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Cf. A079586, A000045.

%K nonn,cons

%O 0,1

%A _Michel Lagneau_, Mar 26 2011

%E Offset corrected by _Arkadiusz Wesolowski_, Jun 28 2011

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Last modified October 17 19:24 EDT 2019. Contains 328127 sequences. (Running on oeis4.)