1. The problem statement, all variables and given/known data series from n = 1 to infinity, (ne^(-n)) 2. Relevant equations 3. The attempt at a solution I want to use integral test. I know this function is: positive (on interval 1 to infinity) continous and finding derivative of f(x) = xe^(-x) I found it to be ultimately decreasing. So integral test is applicable. I set up integral from 1 to infinity (xe^(-x)) u = x du = dx v = -e^(-x) dv = e^(-x) -xe^(-x) + integral e^(-x) -xe^(-x) - e^(-x) = -e^(-x) (x + 1) evaluating from 1 to t [itex] -(1/e^t) (t+1) + 2/e^(1) [/itex] but now when I do lim t -> infinity, -(1/e^t) (t+1) should = infinity/infinity, which would mean [itex] a_n [/itex] would be divergent, but it is convergent. does anyone know where my mistake is??