A216542 Decimal expansion of Sum_{k=1..50000} (-1)^(k-1)/(2k-1).

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

Offset: 0

Author

N. J. A. Sloane, Sep 08 2012

Keywords

• nonn
• cons
• easy

Comments

A deceptively correct-looking approximation to Pi/4. The constant is rational, by definition (a product of finitely many rational numbers).

Examples

			Pi/4:     0.785398163397448309615660845819875721049292349843776455...
This sum: 0.785393163397448809615660595819876026049291657343778981...
..........=================^========^^======^^=^=====^^^^^====^^^^...
		

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 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.

Crossrefs

Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.

Cf. also A195793.

Programs

Maple

Digits:=300; M:=50000; add(evalf((-1)^(k-1)/(2*k-1)), k=1..M);

Mathematica

First[RealDigits[Sum[(-1)^(k-1)/(2*k-1), {k, 50000}], 10, 100]] (* Paolo Xausa, Apr 23 2024 *)

Formula

Equals A013706/2. - Hugo Pfoertner, Apr 23 2024