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%I #24 Apr 17 2024 11:02:23
%S 2,1,6,7,4,3,2,4,6,8,3,4,9,7,7,7,5,9,3,9,3,4,9,8,7,9,0,9,7,0,7,1,7,6,
%T 7,8,4,1,3,0,4,3,8,4,1,8,3,6,3,1,1,2,2,6,0,8,3,7,5,7,9,5,9,7,2,9,4,0,
%U 9,8,3,7,8,5,2,7,3,5,3,3,2,2,6,3,9,3,7
%N Decimal expansion of Sum_{i>=0} 1/((8*i+1)*(8*i+5)).
%H Vincenzo Librandi, <a href="/A196554/b196554.txt">Table of n, a(n) for n = 0..10000</a>
%H L. B. W. Jolley, <a href="https://archive.org/details/summationofserie00joll">Summation of Series</a>, Dover, 1961, eq. 266 p. 48.
%F Equals sqrt(2)*(Pi + log(3 + 2^(3/2)))/32.
%e 0.21674324683497 = 1/5 + 1/117 + 1/357 + 1/725 + 1/1221 + 1/1845 + ...
%p sqrt(2)/32*(Pi+log(3+2*sqrt(2))) ; evalf(%) ;
%t RealDigits[(Sqrt[2]/32)(Pi + Log[3 + 2 Sqrt[2]]), 10, 74][[1]] (* _Bruno Berselli_, Dec 20 2011 *)
%K cons,easy,nonn
%O 0,1
%A _R. J. Mathar_, Oct 03 2011
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