# Property of convergent series. [duplicate]

If $\sum a(n)$ and $\sum b(n)$ are convergent series with positive terms,can I say that $\sum a(n)b(n)$ is also convergent?

• Since $\sum_n |a_n| < \infty$, it suffices that $b(n)$ is bounded to obtain $\sum_n |a_n b_n| < \infty$, no need that $b(n) \to 0$ or $\sum_n b(n) < \infty$. – reuns Nov 18 '17 at 21:21
• Yes, you can.${}{}{}{}{}$ – DonAntonio Nov 18 '17 at 21:21