1. The problem statement, all variables and given/known data Find the interval of convergence for the following power series. Specify both absolute and conditional convergence where appropriate. 2. Relevant equations 1 + x + 2x^2 + 6x^3 + ... + n! x^n + ... 3. The attempt at a solution Using the ratio test to determine convergence of the series, I have the following: (n+1)! x^(n+1)/[n! x^n] = (n!)(x^(n+1))/[(n!)(x^n)] = x(n+1) (After cancellation of factorials) = x * lim n->∞ (n+1) x < 1 converges x > 1 diverges Series does not converge? I'm not sure if my answer is right or not. Any help is much appreciated. Thanks!