Example 4.23.  The infinite series    has radius of convergence by the ratio test because

            .

Since the limit equals  0,  we set  .    

Explore Solution 4.23.

Enter the formula for the coefficients.

Use d'Alembert's ratio test and find the limit and then the radius of convergence R.

The sum of the series is a well known function.

We can plot some of the partial sums and see that they converge to f[z].

(c) 2006 John H. Mathews, Russell W. Howell