Here's the problem transcribed from the book:
Use the Borel Cantelli lemma to prove that given any sequence of random variables $\{X_n, n \ge 1\}$ whose range is the real line, there exist constants $c_n \to \infty$ such that $ P[\lim_{n \to \infty} \frac{X_n}{c_n}=0] = 1. $
Give a careful description of how you choose $c_n$.
Basically I get confused when I think about picking a $c_n$ such that $\sum P(\frac{X_n}{c_n} \ge \epsilon) < \infty$.