intergral test for convergence of the series

Question

Use the integral test to establish the convergence of the series which is the sum from n=1 to infinity of the terms a_n=e^-n

Answer 1

∫₀^∞e^-ndn = -(e^-n)₀^∞ = -e^-∞ +1 = 1- 1/e^∞ =1-0= 1 which establishes convergence.