Answer
(a) General form of power series is: $ \Sigma_{n=0}^\infty c_n(x-a)^n$(centered at $a$).
(b) The radius of convergence of the power series $ \Sigma_{n=0}^\infty c_n(x-a)^n$(centered at $a$) is a positive number $\bf{R}$ such that the series converges if $|x-a| \lt \bf{R}$ and diverges if $|x-a| \gt \bf{R}$.
(c) The interval of convergence of a power series is the interval that consists of all values of $x$ for which the series converges.
Work Step by Step
(a) General form of power series is: $ \Sigma_{n=0}^\infty c_n(x-a)^n$(centered at $a$).
(b) The radius of convergence of the power series $ \Sigma_{n=0}^\infty c_n(x-a)^n$(centered at $a$) is a positive number $\bf{R}$ such that the series converges if $|x-a| \lt \bf{R}$ and diverges if $|x-a| \gt \bf{R}$.
(c) The interval of convergence of a power series is the interval that consists of all values of $x$ for which the series converges.
