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Decimal expansion of Sum_{k>=1} (2^k - 1)/(3^k - 1).
5

%I #7 Aug 02 2024 12:10:01

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

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

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

%N Decimal expansion of Sum_{k>=1} (2^k - 1)/(3^k - 1).

%H R. J. Mathar, <a href="/A372907/a372907.pdf">Resummation, acceleration of convergence</a>

%e 1.7212997093744468397666319454096698915574145419799...

%t s = Sum[(2^k - 1)/(3^k - 1), {k, 1, 800}];

%t d = N[s, 100]

%t First[RealDigits[d]]

%Y Cf. A372908.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Jun 12 2024