A331239 Decimal expansion of Sum_{k>=0} (-1)^k/AGM(1, 1+k).

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

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

Table of n, a(n) for n=0..86.

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