## Calculus 8th Edition

(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.
(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.