converges or diverges?

Question

Determine whether the series converges or diverges

sum from n=1 to infinity ((e^(1/n))/n)

Answer 1

∑₁^∞e^1/n/n.

Let using limit comparison test with divergent harmonic series: lim n →∞ (e^1/n/n)/(1/n) = lim n → ∞ e^1/n = e⁰ = 1. So, by comparison test given series also diverges