%I #31 Apr 23 2024 08:10:42

%S 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,

%T 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,

%U 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

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

%C A deceptively correct-looking approximation to Pi/4.

%H J. M. Borwein, P. B. Borwein and K. Dilcher, <a href="http://www.jstor.org/stable/2324715">Pi, Euler numbers and asymptotic expansions</a>, Amer. Math. Monthly, 96 (1989), 681-687.

%H J. M. Borwein and R. M. Corless, <a href="http://www.cecm.sfu.ca/~jborwein/sloane/sloane.html">Review of "An Encyclopedia of Integer Sequences" by N. J. A. Sloane and Simon Plouffe</a>, SIAM Review, 38 (1996), 333-337.

%F Equals A013706/2. - _Hugo Pfoertner_, Apr 23 2024

%e Pi/4: 0.785398163397448309615660845819875721049292349843776455...

%e This sum: 0.785393163397448809615660595819876026049291657343778981...

%e ..........=================^========^^======^^=^=====^^^^^====^^^^...

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

%t First[RealDigits[Sum[(-1)^(k-1)/(2*k-1), {k, 50000}], 10, 100]] (* _Paolo Xausa_, Apr 23 2024 *)

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

%Y Cf. also A195793.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Sep 08 2012