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A145424
Decimal expansion of Sum_{n>=1} 1/(n*(25n^2-1)).
0
0, 4, 9, 8, 0, 8, 5, 6, 6, 7, 4, 7, 6, 3, 0, 5, 1, 6, 8, 6, 2, 7, 4, 0, 7, 0, 7, 7, 2, 0, 9, 9, 1, 3, 3, 1, 1, 8, 7, 7, 1, 5, 0, 4, 6, 0, 1, 1, 0, 0, 9, 2, 2, 0, 8, 3, 7, 0, 6, 7, 4, 9, 4, 3, 3, 3, 4, 2, 5, 2, 5, 3, 9, 6, 0, 9, 8, 7, 1, 5, 7, 4, 8, 9, 5, 3, 0, 1, 7, 8, 4, 8, 7
OFFSET
0,2
REFERENCES
Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, 1996, 4.1.26.
FORMULA
Equals log(phi)*sqrt(5)/2 - 5*(2 - log(5))/4, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2024
EXAMPLE
0.049808566747630516862...
MAPLE
evalf(5*log(5)/4-5/2+sqrt(5)/2*log((1+sqrt(5))/2)) ;
MATHEMATICA
RealDigits[Log[GoldenRatio]*Sqrt[5]/2 - 5*(2 - Log[5])/4, 10, 120, -1][[1]] (* Amiram Eldar, Aug 23 2024 *)
CROSSREFS
Sequence in context: A205297 A159643 A200398 * A200394 A249272 A280630
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Feb 08 2009
STATUS
approved