# Cauchy Product of Absolutely Convergent Series

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## Theorem

Let $\displaystyle \sum_{n \mathop = 0}^\infty a_n$ and $\displaystyle \sum_{n \mathop = 0}^\infty b_n$ be two real series that are absolutely convergent.

Then the Cauchy product of $\displaystyle \sum_{n \mathop = 0}^\infty a_n$ and $\displaystyle \sum_{n \mathop = 0}^\infty b_n$ is absolutely convergent.

## Proof

## Sources

- 1992: Larry C. Andrews:
*Special Functions of Mathematics for Engineers*... (previous) ... (next): $\S 1.2.3$: Operations with series: Theorem $1.7$