What is the radius of convergence of #sum_1^oo e^(nx) / 2^(2n)?#? Calculus Power Series Determining the Radius and Interval of Convergence for a Power Series 1 Answer Cesareo R. Jul 18, 2016 #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# Answer link Related questions How do you find the radius of convergence of a power series? How do you find the radius of convergence of the binomial power series? What is the radius of convergence for a power series? What is interval of convergence for a Power Series? How do you find the interval of convergence for a power series? How do you find the radius of convergence of #sum_(n=0)^oox^n# ? What is the radius of convergence of the series #sum_(n=0)^oo(x-4)^(2n)/3^n#? How do you find the interval of convergence for a geometric series? What is the interval of convergence of the series #sum_(n=0)^oo((-3)^n*x^n)/sqrt(n+1)#? What is the radius of convergence of the series #sum_(n=0)^oo(n*(x+2)^n)/3^(n+1)#? See all questions in Determining the Radius and Interval of Convergence for a Power Series Impact of this question 2156 views around the world You can reuse this answer Creative Commons License