cp's OEIS Frontend

A013706 Decimal expansion of 2*Sum_{k=1..50000} (-1)^(k-1)/(2k-1).

%I A013706 #37 Apr 23 2024 11:21:09
%S A013706 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 A013706 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 A013706 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 A013706 Decimal expansion of 2*Sum_{k=1..50000} (-1)^(k-1)/(2k-1).
%C A013706 A deceptively correct-looking approximation to Pi/2.
%H A013706 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 A013706 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 A013706 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 A013706 Pi/2:     1.570796326794896619231321691639751442098584699687552910487472...
%e A013706 This sum: 1.570786326794897619231321191639752052098583314687557962587445...
%e A013706 ..........================^=================^^^======^^^^=====^=^^^===^^...
%t A013706 RealDigits[2*Sum[(-1)^(k-1)/(2k-1),{k,50000}],10,130][[1]] (* _Harvey P. Dale_, Oct 23 2012 *)
%Y A013706 Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.
%Y A013706 Cf. also A013707, A195793.
%K A013706 cons,nonn,easy,nice
%O A013706 1,2
%A A013706 _N. J. A. Sloane_
%E A013706 Entry revised by _N. J. A. Sloane_, Sep 08 2012