%I #27 Dec 17 2022 03:31:20

%S 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,

%T 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,

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

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

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

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

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

%e 0.0568528194400546905827678785418234319244998656397447458793199905066...

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

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

%o (PARI) 3/4 - log(2) \\ _Charles R Greathouse IV_, Jul 14 2014

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

%K nonn,cons

%O 0,2

%A _Bruno Berselli_, Mar 16 2014