A201616 Decimal expansion of Sum_{n = 1 .. infinity} (-1)^(n+1)/F(n)^n where F=A000045 is the Fibonacci sequence.

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

Offset: 0

Author

Michel Lagneau, Dec 03 2011

Keywords

• nonn
• cons

Examples

			0.1129705222005977422380406779... = 1/1^1 - 1/1^2 + 1/2^3 - 1/3^4 + 1/5^5 - ...
		

Crossrefs

Cf. A079586, A158933, A000045, A201615.

Programs

Maple

with(combinat,fibonacci):Digits:=120:s:=sum( evalf(((-1)^(n+1))/ fibonacci(n)^n),n=1..200):print(s):

Mathematica

RealDigits[N[Sum[((-1)^(n+1))/Fibonacci[n]^n,{n,1,105}],105]][[1]]

PARI

-suminf(n=1,(-1)^n/fibonacci(n)^n) \\ Charles R Greathouse IV, Dec 05 2011