A013707 Decimal expansion of Sum_{k=1..50000} (-1)^(k+1) / k.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• cons
• nonn
• easy
• nice

Links

• J. M. Borwein, P. B. Borwein and K. Dilcher, Pi, Euler numbers and asymptotic expansions, Amer. Math. Monthly, 96 (1989), 681-687.
• J. M. Borwein, P. B. Borwein and K. Dilcher, Pi, Euler numbers and asymptotic expansions, Amer. Math. Monthly, 96 (1989), 681-687.
• J. M. Borwein and R. M. Corless, Review of "An Encyclopedia of Integer Sequences" by N. J. A. Sloane and Simon Plouffe, SIAM Review, 38 (1996), 333-337.

Crossrefs

Cf. A013705, A013706.

Programs

Mathematica

RealDigits[Sum[(-1)^(k+1)/k,{k,50000}],10,120][[1]] (* Harvey P. Dale, Jul 27 2017 *)

Formula

log(2) + (Psi(25000 + 1/2) - Psi(25001))/2. - Robert Israel, Feb 03 2015

Extensions

Corrected and extended by Jon E. Schoenfield, Feb 03 2015