A257960 Decimal expansion of Sum_{n>=3} (-1)^n/log(log(log(n))).

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

Table of n, a(n) for n=3..111.

Eric Weisstein's World of Mathematics, Leibniz Criterion.

Wikipedia, Alternating series test.

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

Cf. A099769, A257837, A257812, A257898.

Sequence in context: A330479 A349804 A355500 * A238734 A332633 A316352

Adjacent sequences: A257957 A257958 A257959 * A257961 A257962 A257963

Keyword

nonn,cons

Author

Iaroslav V. Blagouchine, May 14 2015

Status

approved