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# Describe the radius of convergence of a power series. Describe the interval of convergence of a power series.

Solution

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To describe the radius of convergence and the interval of convergence of a power series, we will refer to the book (chapter $9$, page $660$):

The number $R$ is the radius of convergence of the power series. If the series converges only at $c$, the radius of convergence is $R=0$, and if the series converges for all $x$ the radius of convergence is $R=\infin$. The set of all values of $x$ for which the power series converges is the interval of convergence of the power series.

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