1. The problem statement, all variables and given/known data Does this series converge or diverge? Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1) 2. Relevant equations 3. The attempt at a solution Okay, I've tried it both ways. Ratio test: lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1)) Now, that doesn't appear to simplify in anyway that would make using l'hospital's rule possible to find the limit. Root test: lim n --> inf. of -3*n^(1/n) / 4^((n-1)/n) That bottom part throws me off.