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%I #18 Feb 01 2020 02:07:48
%S 6,0,9,2,1,5,1,5,0,4,5,2,4,4,9,2,2,8,7,3,0,4,7,3,3,7,1,3,4,9,1,6,6,0,
%T 5,1,1,1,8,3,9,3,9,2,2,8,5,6,5,9,9,9,7,3,5,7,8,7,2,0,3,1,3,8,1,9,5,6,
%U 7,5,6,0,2,5,4,2,6,7,1,2,2,7,6,1,2,3,0
%N Decimal expansion of Sum_{k>=0} (-1)^k/AGM(1, 1+k).
%C AGM(x, y) is the arithmetic-geometric mean of Gauss and Legendre.
%C This series is closely related to A188859 (Sum_{k>=0} (-1)^k/((1+(1+k))/2)) and A113024 (Sum_{k>=0} (-1)^k/sqrt(1+k)). The denominators of these alternating series differ by being arithmetic, geometric, or arithmetic-geometric means of 1 and k.
%e 0.6092151504524492287304733713491660511183939228565999735...
%o (PARI) sumalt(k=0, (-1)^k/agm(1,1+k))
%Y Cf. A016627, A188859, A113024.
%K nonn,cons
%O 0,1
%A _Daniel Hoyt_, Jan 13 2020
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