Power series/R/Same variable/Cauchy product/Exercise

Let ${}\sum _{n=0}^{\infty }a_{n}x^{n}$ and ${}\sum _{n=0}^{\infty }b_{n}x^{n}$ be two power series absolutely convergent in ${}x\in \mathbb {R}$. Prove that the Cauchy product of these series is exactly

$\sum _{n=0}^{\infty }c_{n}x^{n}{\text{ where }}c_{n}=\sum _{i=0}^{n}a_{i}b_{n-i}.$

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