"Suppose $\displaystyle \sum a_n, \sum b_n$ are convergent. Let $\displaystyle c_n=\sum_{k=0}^n a_kb_{n-k}$ and let $\displaystyle \sum c_n$ converge. Prove that$\displaystyle (\sum_0^\infty a_n) (\sum_0^\infty b_n) = (\sum_0^\infty c_n).$"

I can't make any headways. Any hints would be appreciated.