1. Power Series http://calculusapplets.com/powerseries.html
If x is a variable, then an infinite series of the form
Is called a power series. More generally, series of the form
Is called a power series center at c, where c is a constant.

2. Convergence of a Power Series
For a power series center at c, precisely one of the following is true.
The series converges only at c.
There exists a real number R>0 such that the series converges absolutely for |x – c| < R, and diverges for |x – c| > R.
The series converges absolutely for all x.
The number R is the radius of convergence of the power series. The set of all values of x for which the power series converges is the interval of convergence of the power series

3. Find where the power series is center and radius of convergence

4. Find the radius of convergence of

5. Find where the radius of convergence of the power series

6. Find the interval of convergence for

7. Find the interval of convergence for
Ans: (-3, 1)

8. Find the interval of convergence for
Ans: [-1,1]