Let $\displaystyle \sum_{k=1}^{\infty}a_n$ be a convergent series.

Let $\displaystyle |\frac{a_{n+1}}{a_n}| < r < 1$ , $\displaystyle n \in N$.

Let $\displaystyle (b_n)$ be a sequence such that $\displaystyle |b_n|< M$.

Prove that $\displaystyle \sum_{k=1}^{\infty}a_n b_n$ is convergent.

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I see here that

$\displaystyle |\frac{a_{n+1}}{a_n}| < r < 1$ looks like the ratio test.

$\displaystyle (b_n)$ has upperbound M.

How do I go about this proof?