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Decimal expansion of Sum_{k=1..5000000} (-1)^(k-1)/(2k-1).
10

%I #22 Oct 09 2015 08:21:13

%S 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,

%T 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,

%U 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

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

%C An 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.

%e 0.7853981133974483096161608458198756960492923498468264552437...

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

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

%Y Cf. A003881, 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