A351687 Decimal expansion of Sum_{n>=2} (-1)^n/log(n!).

1, 0, 7, 6, 9, 0, 1, 0, 2, 7, 8, 5, 8, 6, 3, 1, 4, 7, 1, 9, 9, 7, 3, 7, 4, 8, 2, 0, 7, 3, 3, 2, 8, 7, 9, 3, 8, 2, 9, 4, 8, 1, 2, 6, 4, 6, 7, 7, 7, 6, 4, 1, 6, 1, 1, 6, 9, 8, 7, 9, 4, 7, 8, 9, 6, 4, 4, 2, 1, 7, 4, 1, 1, 1, 1, 4, 0, 4, 3, 6, 6, 6, 6, 9, 7, 1, 8, 3, 7, 5, 3, 9, 5, 7, 9, 0

Offset: 1

Author

Bernard Schott, May 05 2022

Keywords

• nonn
• cons

Comments

This series is convergent according to the alternating series test, while series Sum_{n>=2} 1/log(n!) -> infinity (link).

Examples

			1.0769010278586314719973748207332879382948126467776416116987...
		

Links

• Socratic Q&A, How do you test the Series Sum_{n>=2} 1/log(n!) for convergence?

Crossrefs

Cf. A099769 (Sum_{n>=2} (-1)^n/log(n)).

Cf. A099871, A257898, A257960, A336741.

Programs

Maple

evalf(sum((-1)^n / log(n!),n=2..infinity),120);

Mathematica

RealDigits[NSum[(-1)^k/Log[k!], {k, 2, Infinity}, WorkingPrecision -> 120, Method -> "AlternatingSigns"]][[1]] (* Amiram Eldar, May 05 2022 *)

PARI

sumalt(k=2, (-1)^k/log(k!)) \\ Vaclav Kotesovec, May 05 2022

Formula

Equals Sum_{k>=2} (-1)^k/log(k!).