Prove that exists a sequence such that $\lim_{n \rightarrow \infty}c_n= \infty$ and $ \sum_{n=1}^{\infty}c_n a_n < \infty $
Prove that $\exists \{c_n\}$ monotonically increasing to $\infty$ such that $\sum_{i=1}^\infty a_nc_n$ coverges.