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A201616
Decimal expansion of Sum_{n = 1 .. infinity} (-1)^(n+1)/F(n)^n where F=A000045 is the Fibonacci sequence.
1
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
0,3
EXAMPLE
0.1129705222005977422380406779... = 1/1^1 - 1/1^2 + 1/2^3 - 1/3^4 + 1/5^5 - ...
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]]
PROG
(PARI) -suminf(n=1, (-1)^n/fibonacci(n)^n) \\ Charles R Greathouse IV, Dec 05 2011
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Michel Lagneau, Dec 03 2011
STATUS
approved