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 A331239 Decimal expansion of Sum_{k>=0} (-1)^k/AGM(1, 1+k). 0
 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, 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, 7, 5, 6, 0, 2, 5, 4, 2, 6, 7, 1, 2, 2, 7, 6, 1, 2, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS AGM(x, y) is the arithmetic-geometric mean of Gauss and Legendre. 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. LINKS EXAMPLE 0.6092151504524492287304733713491660511183939228565999735... PROG (PARI) sumalt(k=0, (-1)^k/agm(1, 1+k)) CROSSREFS Cf. A016627, A188859, A113024. Sequence in context: A085673 A117492 A022903 * A324008 A248681 A232815 Adjacent sequences:  A331236 A331237 A331238 * A331240 A331241 A331242 KEYWORD nonn,cons AUTHOR Daniel Hoyt, Jan 13 2020 STATUS approved

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Last modified January 23 16:17 EST 2021. Contains 340385 sequences. (Running on oeis4.)