A216546 Decimal expansion of Sum_{k=1..5000000} (-1)^(k-1)/(2k-1).

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

Offset

0,1

Comments

An approximation to Pi/4. The constant is rational, by definition (a product of finitely many rational numbers).

Links

Table of n, a(n) for n=0..123.

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.

Index entries for linear recurrences with constant coefficients.

Example

0.7853981133974483096161608458198756960492923498468264552437...

Maple

Digits:=300; M:=5000000; add(evalf((-1)^(k-1)/(2*k-1)), k=1..M);

Mathematica

RealDigits[Total[Table[(-1)^(k-1)/(2k-1), {k, 5*10^6}]], 10, 130][[1]] (* Harvey P. Dale, May 06 2015 *)

Crossrefs

Cf. A003881, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.

Cf. also A195793.

Sequence in context: A190573 A216542 A216544 * A003881 A225404 A320413

Adjacent sequences: A216543 A216544 A216545 * A216547 A216548 A216549

Keyword

nonn,cons,easy

Author

N. J. A. Sloane, Sep 08 2012

Status

approved