cp's OEIS Frontend

A262023 Decimal expansion of 3*log(2)/2.

%I A262023 #40 Feb 16 2025 08:33:27
%S A262023 1,0,3,9,7,2,0,7,7,0,8,3,9,9,1,7,9,6,4,1,2,5,8,4,8,1,8,2,1,8,7,2,6,4,
%T A262023 8,5,2,1,1,3,2,5,0,2,0,1,5,4,0,3,8,2,8,8,1,1,8,1,0,2,0,0,1,4,2,4,0,0,
%U A262023 9,0,4,3,2,9,5,4,5,4,2,0,7,3,4,0,8,7,9,4,9,9,0,4,9,4,6,2,8
%N A262023 Decimal expansion of 3*log(2)/2.
%C A262023 This is the limit of the reordered alternating harmonic series 1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + 1/9 + 1/11 - 1/6 + ... + ... - ..., with partial sums given in A262031/A262022. This shows that the alternating harmonic series is conditionally convergent. For original references on such series see A262031.
%H A262023 Srinivasa Ramanujan, <a href="https://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/question/q260.htm">Question 260</a>, Journal of the Indian Mathematical Society, Vol. 3 (1911), p. 43.
%H A262023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConditionalConvergence.html">Conditional Convergence</a>.
%H A262023 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A262023 Equals 3*A002162/2.
%F A262023 Equals A016631/2.
%F A262023 3*log(2)/2 = (3/2)*Sum_{n>=1} (-1)^(n+1)/n = Sum_{n>=1} ((-1)^(n+1)/n + (-1)^(n+1)/(2*n)) = A002162 + (A016655/10). - _Terry D. Grant_, Jul 24 2016
%F A262023 Equals 1 + Sum_{k>=1} 2/((4*k)^3 - 4*k) (Ramanujan, 1911). - _Amiram Eldar_, Jan 01 2025
%e A262023 1.039720770839917964125848182187264852113250201540382881181020014240...
%t A262023 First@ RealDigits@ N[3 Log[2]/2, 120] (* _Michael De Vlieger_, Jul 26 2016 *)
%o A262023 (PARI) 3*log(2)/2 \\ _Michel Marcus_, Sep 13 2015
%o A262023 (Magma) 3*Log(2)/2; // _Vincenzo Librandi_, Jan 01 2025
%Y A262023 Cf. A002162, A016631, A016655, A262031, A262022.
%K A262023 nonn,cons,easy
%O A262023 1,3
%A A262023 _Wolfdieter Lang_, Sep 08 2015