Question

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

Answer 1

`x < log_e 4`

Explanation:

`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`