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

%I A216542 #33 Feb 04 2025 10:03:52
%S A216542 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 A216542 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 A216542 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 A216542 Decimal expansion of Sum_{k=1..50000} (-1)^(k-1)/(2k-1).
%C A216542 A deceptively correct-looking approximation to Pi/4. The constant is rational, by definition (a product of finitely many rational numbers).
%H A216542 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 A216542 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.
%H A216542 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>.
%F A216542 Equals A013706/2. - _Hugo Pfoertner_, Apr 23 2024
%e A216542 Pi/4:     0.785398163397448309615660845819875721049292349843776455...
%e A216542 This sum: 0.785393163397448809615660595819876026049291657343778981...
%e A216542 ..........=================^========^^======^^=^=====^^^^^====^^^^...
%p A216542 Digits:=300; M:=50000; add(evalf((-1)^(k-1)/(2*k-1)), k=1..M);
%t A216542 First[RealDigits[Sum[(-1)^(k-1)/(2*k-1), {k, 50000}], 10, 100]] (* _Paolo Xausa_, Apr 23 2024 *)
%Y A216542 Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.
%Y A216542 Cf. also A195793.
%K A216542 nonn,cons,easy
%O A216542 0,1
%A A216542 _N. J. A. Sloane_, Sep 08 2012