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A229020
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Decimal expansion of 1 - 1/(1*2) + 1/(1*2*2) - 1/(1*2*2*3) + ...
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11
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6, 8, 8, 9, 4, 8, 4, 4, 7, 6, 9, 8, 7, 3, 8, 2, 0, 4, 0, 5, 4, 9, 5, 0, 0, 1, 5, 8, 1, 1, 8, 6, 7, 1, 0, 5, 3, 3, 1, 3, 6, 2, 9, 4, 3, 2, 8, 9, 9, 2, 2, 4, 0, 6, 9, 3, 8, 5, 5, 1, 7, 6, 7, 0, 5, 5, 7, 6, 0, 3, 0, 5, 6, 9, 7, 3, 1, 5, 1, 5, 7, 6, 1, 3, 3, 9, 4, 9, 4, 0, 9, 6, 2, 2, 5, 6, 9, 7, 3, 7, 4, 6, 8, 3, 9, 1, 0, 7, 1, 3, 2, 5, 5
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OFFSET
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0,1
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COMMENTS
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As a sum of positive terms, the constant equals Sum_{k >= 1} k/(k!*(k+1)!). If we set S(n) = Sum_{k >= 0} k^n/(k!*(k+1)!) for n >= 0, so this constant is S(1), then S(n) is an integral linear combination of S(0) and S(1). For example S(7) = 16*S(0) + 11*S(1). Cf. A086880. S(0) is A096789.
The Pierce expansion of this constant begins [1, 3, 14, 15, 26, 40, 43, 71, 83, 8120, ...] giving the alternating series representation for this constant 1 - 1/3 + 1/(3*14) - 1/(3*14*15) + 1/(3*14*15*26) - .... (End)
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LINKS
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FORMULA
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Equals exp(-2) * Sum_{k>=0} binomial(2*k,k)/(k+1)!. - Amiram Eldar, Jun 12 2021
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EXAMPLE
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0.68894844769873820405495001581186710536...
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MATHEMATICA
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digits = 113; NSum[(-1)^(n+1)*1/Product[1+Floor[k/2], {k, 1, n}], {n, 1, Infinity}, NSumTerms -> digits, Method -> "AlternatingSigns", WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 21 2014 *)
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PROG
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(PARI) suminf(n=1, (-1)^(n+1)*1./prod(i=1, n, 1+floor(i/2)))
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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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