What is the radius of convergence of $sum_1^oo e^(nx) / 2^(2n)?$ ?

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Answer 1 · 2016-07-18T20:17:12

$x < log_e 4$

$S(x)=sum_1^oo e^(nx) / 2^(2n)=sum_1^oo(e^x/4)^n$

this series converges for $e^x/4 <1$ giving as result

$S(x) = 1/(1-e^x/4) = 4/(4-e^x), forall x | e^x<4->x < log_e 4$

What is the radius of convergence of sum_1^oo e^(nx) / 2^(2n)?sum_1^oo e^(nx) / 2^(2n)??