$\sum_{n=0}^{\infty}c_n(x-a)^n$

where $c_n$ are the coefficients of each term in the series and $a$ is number.

To find the

**Radius of Convergence**of a power series, we need to use the ratio test or the root test. Let $A_n=c_n(x-a)^n$. Then recall that the ratio test is:

$L=\lim$

_{n →$\infty$}$|\frac{A_{n+1}}{A_n}|$

and the root test is

$L=\lim$

_{n →$\infty$}$|A_n|^{\frac{1}{n}}$

where the

**convergence**happens at $L$< $1$ for both tests. More accurately we can say that the

**convergence**happens when $|x-a|$ < $R$, where is the

**Radius of Convergence**.

The

**Interval of Convergence**is the value of all $x$'s, for which the power series converges. So it is important to also check if the power series converges as well at $|x-a|=R$.