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A267316
Decimal expansion of the Dirichlet eta function at 5.
10
9, 7, 2, 1, 1, 9, 7, 7, 0, 4, 4, 6, 9, 0, 9, 3, 0, 5, 9, 3, 5, 6, 5, 5, 1, 4, 3, 5, 5, 3, 4, 6, 9, 5, 3, 2, 5, 5, 3, 5, 1, 3, 3, 6, 2, 0, 3, 3, 0, 4, 3, 2, 6, 1, 2, 2, 5, 8, 0, 5, 6, 3, 5, 5, 3, 4, 8, 1, 5, 8, 6, 5, 4, 2, 4, 6, 3, 8, 8, 9, 1, 7, 7, 5, 0, 4, 0, 4, 1, 2, 3, 9, 7, 3, 1, 2, 5, 0, 2, 8, 5, 5, 8, 9, 4, 0, 7, 0, 1, 2, 4, 8, 9, 6, 8, 2, 0, 9, 7, 7
OFFSET
0,1
LINKS
FORMULA
Equals Sum_{k > 0} (-1)^(k+1)/k^5 = (15*zeta(5))/16.
Equals Lim_{n -> infinity} A136676(n)/A334604(n). - Petros Hadjicostas, May 07 2020
EXAMPLE
1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 + ... = 0.972119770446909305935655143553469532553513362...
MATHEMATICA
RealDigits[(15 Zeta[5])/16, 10, 120][[1]]
PROG
(PARI) 15*zeta(5)/16 \\ Michel Marcus, Feb 01 2016
(Sage) s = RLF(0); s
RealField(110)(s)
for i in range(1, 10000): s += -((-1)^i/((i)^5))
print(s) # Terry D. Grant, Aug 05, 2016
CROSSREFS
Cf. A002162 (value at 1), A013663, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A136676, A334604.
Sequence in context: A083995 A195357 A328968 * A346907 A021511 A029688
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Jan 13 2016
STATUS
approved