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Decimal expansion of 2*Sum_{k=1..50000} (-1)^(k-1)/(2k-1).
11

%I #37 Apr 23 2024 11:21:09

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

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

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

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

%C A deceptively correct-looking approximation to Pi/2.

%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, P. B. Borwein and K. Dilcher, <a href="/A013706/a013706.png">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 Pi/2: 1.570796326794896619231321691639751442098584699687552910487472...

%e This sum: 1.570786326794897619231321191639752052098583314687557962587445...

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

%t RealDigits[2*Sum[(-1)^(k-1)/(2k-1),{k,50000}],10,130][[1]] (* _Harvey P. Dale_, Oct 23 2012 *)

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

%Y Cf. also A013707, A195793.

%K cons,nonn,easy,nice

%O 1,2

%A _N. J. A. Sloane_

%E Entry revised by _N. J. A. Sloane_, Sep 08 2012