1. The problem statement, all variables and given/known data Determine the radius of convergence of the given power serie . Ʃ(x^(2n))/n! n goes from 0 to infinity 2. Relevant equations limit test ratio 3. The attempt at a solution I am using the limit test ratio and I've got this : [n! * x^(2n+2)]/[(n+1)! * x^2n], then [n!* x^2n * x^2]/[(n+1) * n! * x^2n] , canceling the common things I am left with lim n-> infinity of x^2/n+1, which is 0, but the radius of convergence is infinity, why is infinity?