1. The problem statement, all variables and given/known data Determine whether the series converges or diverges. ∞ ∑ 1/n! n=1 2. Relevant equations If ∑bn is convergent and an≤bn for all n, then ∑an is also convergent. Suppose that ∑an and ∑bn are series with positive terms. If lim an = C n→∞ bn where c is finite number and c>o, then either both series converge or both diverge. 3. The attempt at a solution So I said: 1/n! < 1/n . And 1/n diverges because it is a harmonic series. Then I tried the limit comparison test... lim (1/n!)/(1/n) = ∞/o. n→∞ I want to use the L'Hospital rule...but I have no clue how to derive that. The book says the answer is convergent...I'm not sure if I'm missing something. Thanks for your help!