A324007 Decimal expansion of the sum of reciprocals of the products of 3 consecutive Fibonacci numbers.
7, 1, 0, 8, 5, 5, 3, 5, 1, 4, 2, 9, 3, 2, 8, 4, 1, 6, 8, 8, 7, 6, 9, 4, 4, 9, 0, 3, 8, 4, 2, 7, 0, 8, 3, 3, 0, 4, 5, 1, 1, 8, 0, 4, 8, 4, 1, 0, 3, 0, 8, 6, 3, 9, 9, 7, 4, 9, 7, 3, 5, 1, 4, 9, 3, 6, 9, 6, 4, 2, 3, 8, 2, 6, 1, 1, 3, 5, 4, 4, 8, 4, 1, 7, 5, 8, 8, 4, 1, 6, 8, 1, 7, 1, 4, 8, 5, 8, 5, 7, 6, 8, 5, 4, 9
Offset: 0
Examples
0.71085535142932841688769449038427083304511804841030863997497351493696423826...
Links
- Brother Alfred Brousseau, Summation of Infinite Fibonacci Series, The Fibonacci Quarterly, Vol. 7, No. 2 (1969), pp. 143-168.
- R. S. Melham, On Some Reciprocal Sums of Brousseau: An Alternative Approach to That of Carlitz, Fibonacci Quarterly, Vol. 41, No. 1 (2003), pp. 59-62.
Programs
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Mathematica
RealDigits[ Sum[ N[ 1/Product[ Fibonacci@j, {j, k, k + 2}], 128], {k, 177}], 10, 111][[1]] -
PARI
suminf(n=1, 1/(fibonacci(n)*fibonacci(n+1)*fibonacci(n+2))) \\ Michel Marcus, Feb 19 2019
Formula
From Amiram Eldar, Feb 09 2023: (Start)
Equals Sum_{k>=1} 1/A065563(k).
Equals 1 - A158933 (Melham, 2003). (End)