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A351222
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Decimal expansion of Sum_{k>=0} (-1)^k/Fibonacci(4*k+2).
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0
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8, 9, 0, 8, 6, 7, 0, 2, 1, 9, 7, 2, 1, 1, 8, 2, 6, 0, 0, 4, 8, 8, 5, 1, 5, 2, 9, 2, 4, 1, 5, 6, 8, 0, 2, 0, 4, 3, 0, 5, 1, 2, 8, 4, 4, 1, 5, 8, 2, 0, 4, 3, 4, 5, 6, 6, 2, 0, 8, 0, 2, 7, 1, 9, 7, 5, 5, 2, 1, 5, 5, 6, 7, 2, 2, 1, 9, 9, 7, 5, 7, 6, 0, 5, 3, 1, 7, 8, 8, 3, 4, 9, 1, 6, 6, 2, 6, 7, 9, 5, 8, 5, 9, 2, 6
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OFFSET
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0,1
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LINKS
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Wray G. Brady, Problem B-319, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 13, No. 4 (1975), p. 373; Rerun, Solution to Problem B-319, ibid., Vol. 14, No. 5 (1976), p. 472.
L. Carlitz, Problem B-111, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 5, No. 1 (1967), p. 108; Another Series Equality, Solution to Problem B-110 by the proposer, ibid., Vol. 5, No. 5 (1967), pp. 470-471.
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FORMULA
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Equals sqrt(5) * Sum_{k>=0} 1/Lucas(4*k+2) (Carlitz, 1967).
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EXAMPLE
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0.89086702197211826004885152924156802043051284415820...
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MATHEMATICA
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RealDigits[NSum[(-1)^n/Fibonacci[4*n + 2], {n, 0, Infinity}, WorkingPrecision -> 1200], 10, 100][[1]]
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PROG
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(PARI) sumpos(k=0, (-1)^k/fibonacci(4*k+2)) \\ Michel Marcus, Feb 05 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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