If $\sum_{i=1}^{\infty} a_i< \infty$, find $b_i$ such that $\sum_{i=1}^{\infty} a_i/b_i<\infty$.

Question

Let $\{a_i\}$ be a given sequence of positive numbers such that $\sum_{i=1}^{\infty} a_i < \infty$. Is it always possible to produce a sequence $\{b_i\}$ of positive numbers such that $\sum_{i=1}^{\infty}b_i < \infty$ and $\sum_{i=1}^{\infty}\frac{a_i}{b_i} < \infty?$

I wonder if Kronecker's Lemma can be of help.