%I #19 May 17 2015 12:25:48
%S 1,1,4,7,7,9,6,8,0,1,3,9,8,7,0,7,5,9,1,1,5,0,7,7,8,8,9,6,7,5,6,7,9,6,
%T 1,9,1,6,6,5,1,8,8,6,8,4,3,2,8,7,6,5,2,3,0,3,2,3,1,4,7,6,5,5,4,6,8,5,
%U 6,2,1,0,6,1,4,7,4,7,0,4,4,8,9,6,5,5,8,2,4,0,2,2,1,2,7,6,5,8,9,3,1,6,1,7,7,5,5,8,5
%N Decimal expansion of Sum_{n=2..infinity} (-1)^n/log(log(n)), negated.
%C A very 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 -11.47796801398707591150778896756796191665188684328765...
%p evalf(sum((-1)^n/log(log(n)), n = 2..infinity), 120);
%t NSum[(-1)^n/Log[Log[n]], {n, 2, Infinity}, AccuracyGoal -> 120, Method -> "AlternatingSigns", WorkingPrecision -> 200]
%o (PARI) default(realprecision, 120); sumalt(n=2, (-1)^n/log(log(n)))
%Y Cf. A099769, A257837, A257812.
%K nonn,cons
%O 2,3
%A _Iaroslav V. Blagouchine_, May 12 2015
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