Answer
(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 $\infty$. If the series converges for $|x-a|\lt R$, then R is the radius of convergence.
(b) The interval of convergence is the domain of $x$ for which the power series converges.
Work Step by Step
(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.
