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%I #35 Mar 19 2024 17:25:05
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{n>=3} (-1)^n/log(log(log(n))).
%C An extremely slowly convergent series, converging in virtue of Leibniz's rule.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeibnizCriterion.html">Leibniz Criterion</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Alternating_series_test">Alternating series test</a>.
%e 277.8674989684568172306449945790310149069364211466765...
%p 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.
%t 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 *)
%o (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 */
%Y Cf. A099769, A257837, A257812, A257898.
%K nonn,cons
%O 3,1
%A _Iaroslav V. Blagouchine_, May 14 2015
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