Find the Maclaurin series for the function using definition of a Mclaurin series. Also, find the radius of convergence.
For power series the simplest way to find the radius of convergence is to use the "ratio test".
A series of positive numbers, will converge as long as the sequence has a limit less than 1. (If that limit is larger than 1, it diverges. If it is equal to 1, we don't know.)
Here, . Those terms may not be positive but we know that a power series always converges absolutely inside its radius of convergence so we can take the absolute value:
What is the limit of that as n goes to infinity? For what values of x is that limit less than 1?