4.3  Geometric Series and Convergence Theorems

    We begin this section by presenting a series of the form   ,  which is called a geometric series and is one of the most important series in mathematics.

Real Exploration.

    The complex geometric series is a generalization of the real geometric series    that is studied in calculus.  The partial sums converge to the infinite series    on the interval , and the infinite sum is  .

We can use Mathematica to draw a series of graph which illustrate the convergence of the partial sums to the infinite sum.

The following might give an insight into what happens when a complex number is used instead of a real number.

In this module we extend geometric series to the complex numbers.

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