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A257960
Decimal expansion of Sum_{n>=3} (-1)^n/log(log(log(n))).
7
2, 7, 7, 8, 6, 7, 4, 9, 8, 9, 6, 8, 4, 5, 6, 8, 1, 7, 2, 3, 0, 6, 4, 4, 9, 9, 4, 5, 7, 9, 0, 3, 1, 0, 1, 4, 9, 0, 6, 9, 3, 6, 4, 2, 1, 1, 4, 6, 6, 7, 6, 5, 8, 8, 8, 3, 9, 1, 0, 1, 9, 3, 3, 2, 5, 5, 1, 9, 0, 2, 7, 1, 3, 7, 0, 9, 9, 9, 2, 5, 5, 5, 0, 1, 2, 2, 7, 6, 9, 6, 8, 8, 3, 0, 9, 6, 8, 3, 3, 0, 6, 8, 4, 7, 6, 3, 0, 8, 3
OFFSET
3,1
COMMENTS
An extremely slowly convergent series, converging in virtue of Leibniz's rule.
LINKS
Eric Weisstein's World of Mathematics, Leibniz Criterion.
EXAMPLE
277.8674989684568172306449945790310149069364211466765...
MAPLE
evalf(sum((-1)^n/log(log(log(n))), n = 3..infinity), 120); # Maple 12.0 computes this expression with no problems, but later versions of Maple may have some problems with it.
MATHEMATICA
N[NSum[(-1)^n/Log[Log[Log[n]]], {n, 3, Infinity}, AccuracyGoal -> 500, Method -> "AlternatingSigns", WorkingPrecision -> 1000], 119] (* Mathematica needs higher precision than usual to compute this series *)
PROG
(PARI) default(realprecision, 200); precision(sumalt(n=3, (-1)^n/log(log(log(n)))), 120) /* PARI needs higher precision than usual to compute this series */
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved