login
Decimal expansion of the sum of the reciprocals of the decagonal numbers (A001107).
7

%I #20 Feb 08 2023 23:03:11

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

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

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

%N Decimal expansion of the sum of the reciprocals of the decagonal numbers (A001107).

%C For the partial sums of the reciprocals of the (positive) decagonal numbers see A250551(n+1)/A294515(n), n >= 0. - _Wolfdieter Lang_, Nov 07 2017

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>

%F Sum_{n>0} 1/(4n^2 - 3n) = log(2) + Pi/6, (A002162 + A019673).

%e 1.216745956158244182494339352004760382108361700922772890949837441544696356350....

%t RealDigits[ Log[2] + Pi/6, 10, 111][[1]] (* or *)

%t RealDigits[ Sum[1/(4n^2 - 3n), {n, 1 , Infinity}], 10, 111][[1]]

%o (PARI) log(2)+Pi/6 \\ _Charles R Greathouse IV_, Feb 08 2023

%Y Cf. A001107, A000038, A013661, A244639, A016627, A244645, A244646, A244648, A244649, A250551(n+1)/A294515(n).

%K nonn,cons,easy

%O 1,2

%A _Robert G. Wilson v_, Jul 03 2014