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Decimal expansion of sum_{n >= 1} (sin(2/n))^2.
4

%I #12 Oct 20 2014 18:11:01

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

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

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

%N Decimal expansion of sum_{n >= 1} (sin(2/n))^2.

%H Vaclav Kotesovec, <a href="/A248949/b248949.txt">Table of n, a(n) for n = 1..500</a>

%e 3.0136580258100591762101955819548270224075442567134903998883672964281449...

%p evalf(sum((sin(2/n))^2, n=1..infinity), 120); # _Vaclav Kotesovec_, Oct 20 2014

%t (* N[Sum[Sin[2/n]^2, {n, 1, Infinity}], 120], yields only 25 correct decimals *)

%o (PARI) default(realprecision,120); sumpos(n=1,(sin(2/n))^2) \\ _Vaclav Kotesovec_, Oct 20 2014

%Y Cf. A248946, A248947, A248950.

%K nonn,easy,cons

%O 1,1

%A _Clark Kimberling_, Oct 18 2014