$\sum_{n=N}^{\infty}$

The following series will be analyzed:

$\sum_{n=N}^{\infty} \frac{\left ( x \right )^{2 n - 1}}{9^{n}}$

The following is the radius of convergence:

$\text{Click "Calculate" to begin.}$

The radius of convergence is the distance from the center of a power series to the nearest point where the series converges. It is half the length of the interval of convergence.

To find the radius of convergence, you can find the interval of convergence using the Ratio Test. Add the endpoints of the interval and divide by them by 2 to get the radius of convergence.

An inconclusive result means that the Ratio Test is inconclusive for all values of $x$. In this case, you may need to manually use other convergence tests to determine the radius of convergence. This is common in p-series and other special cases.