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Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n) - 1/(2n+1)))).
2

%I #23 Nov 20 2019 06:14:55

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

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

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

%N Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n) - 1/(2n+1)))).

%C The sequence of real values x(n) = (1 - 1/2)^((1/2 - 1/3)^(...^(1/n - 1/(n+1)))) converges to two different limits depending on whether n is even or odd. This integer sequence gives the decimal expansion of the upper limit, to which the even-indexed terms of {x(n)} converge.

%H Zeraoulia Rafik, <a href="https://math.stackexchange.com/q/2822112/156150">Question on Math Stackexchange</a>

%e 0.85885772008416606762434379473241623070938618180813.....

%o (PARI) my(N=100,y=(1/(N*(N+1)))); forstep(n=N-1,1,-1,y=1/(n*(n+1))^y); y \\ _Michel Marcus_, Nov 08 2019

%Y Cf. A328941.

%K nonn,cons

%O 0,1

%A _R Zeraoulia_, Oct 31 2019

%E More terms from _Jon E. Schoenfield_, Nov 02 2019