1. The problem statement, all variables and given/known data Use the ratio test to find the radius of convergence and the interval of convergence of the power series: [[Shown in attachment]] 2. Relevant equations an+1/an=k Radius of convergence = 1/k Interval of convergence: | x-a |∠ R 3. The attempt at a solution I began by finding the summation which I concluded was: Ʃ (2^n)(x-0)^n / n(factorial) So an+1/an = [2n+1/(n+1)(factorial)] *times* [ n(factorial)/ 2n ] After cancelling, I arrived at 2/(n+1) If that lim n→∞ is taken, it would be 0, meaning the radius of convergence is ∞, and the interval is from -∞ to ∞. Is that true or did I make a mistake, because the website for my homework won't allow me to enter infinity (∞)?