Question of the Day

Given that $\sum\limits_{n=1}^\infty b_n $ is a convergent series of positive terms prove that series $\sum\limits_{n=1}^\infty a_n $ of positive terms will also converge if $\lim\limits_{n \to  \infty } \frac{a_n}{b_n} = L > 0$. Hint: You may use the Direct Comparison Test.