## Calculus 8th Edition

(a) If the power series converges only when $x=a$, then the radius of convergence is 0. If the series converges for all $x$, then the radius of convergence is $\infty$. (b) The interval of convergence is the domain of $x$ for which the power series converges.
(a) The interval of convergence of any power series is of the form $|x-a|\lt R$ Here, $R$ is known as radius of convergence. The interval of convergence is $(m,n)$ and then $R=\frac{(n-m)}{2}$. If the power series converges only when $x=a$, then the radius of convergence is 0. If the series converges for all $x$, then the radius of convergence is $\infty$. (b) The interval of convergence is the domain of $x$ for which the power series converges.