1. The problem statement, all variables and given/known data Determine whether the series converges or diverges Sum from n=1 to infinity ((e^(1/n))/n) 2. Relevant equations I am trying to use the limit comparison test to prove it. 3. The attempt at a solution an = (e^(1/n))/n bn = e/n an/bn = e^(1/n)/e lim n-> infinity an/bn = 1/e Sum from n=1 to infinity e/n is divergent. (e/n = e(1/n). So sum from n=1 to infinity e/n = e*sum from n=1 to infinity 1/n. sum from n=1 to infinity 1/n is divergent because this is a p-series with n^p where p = 1. For p <= 1 the series is divergent.) Since either both an and bn are convergent or both are divergent, an must be divergent as bn is divergent. Thanks for any help.