A239354 Decimal expansion of 3/4 - log(2).

0, 5, 6, 8, 5, 2, 8, 1, 9, 4, 4, 0, 0, 5, 4, 6, 9, 0, 5, 8, 2, 7, 6, 7, 8, 7, 8, 5, 4, 1, 8, 2, 3, 4, 3, 1, 9, 2, 4, 4, 9, 9, 8, 6, 5, 6, 3, 9, 7, 4, 4, 7, 4, 5, 8, 7, 9, 3, 1, 9, 9, 9, 0, 5, 0, 6, 6, 0, 6, 3, 7, 8, 0, 3, 0, 3, 0, 5, 2, 8, 4, 3, 9, 4, 1

Offset

0,2

References

L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 249).

Links

Table of n, a(n) for n=0..84.

Index entries for transcendental numbers

Formula

Equals Sum_{k >= 1} 1/((2*k)*(2*k+1)*(2*k+2)).

Equals Integral_{x = 0..1} Integral_{y = 0..1} (x*y)^2/(x + y)^2 dy dx. - Peter Bala, Dec 12 2022

Example

0.0568528194400546905827678785418234319244998656397447458793199905066...
1/(2*3*4) + 1/(4*5*6) + 1/(6*7*8) + 1/(8*9*10) + 1/(10*11*12) + ...

Mathematica

RealDigits[3/4 - Log[2], 10, 100, -1][[1]]

Prog

(PARI) 3/4 - log(2) \\ Charles R Greathouse IV, Jul 14 2014

Crossrefs

Cf. A187832: Sum_{k>=1} 1/((2k-1)*(2k)*(2k+1)).

Sequence in context: A271571 A349577 A094931 * A011498 A330863 A111514

Adjacent sequences: A239351 A239352 A239353 * A239355 A239356 A239357

Keyword

nonn,cons

Author

Bruno Berselli, Mar 16 2014

Status

approved