Suppose that $(a\_n)$ and $(b\_n)$ be sequences such that $\lim (a\_n)=0$ and $\displaystyle \lim \left( \sum\_{i=1}^n b\_i \right)$ exists. Define $c\_n = a\_1 b\_n + a\_2 b\_{n-1} + \dots + a\_n b\_1$. Prove that $\lim (c\_n)=0$