Science:Math Exam Resources/Courses/MATH105/April 2014/Question 02 (b)/Solution 1
Let be the terms in the series. From the ratio test, we are guaranteed absolute convergence when .
With , we have and thus
We recall that and thus in general . This also means that . Thus,
- .
Computing for all x. Hence, the series converges absolutely for all x-values and the radius of convergence is .