In this example we consider the problem of computing a
*geometric series summation*
for the last time.
We have already seen two algorithms to compute this summation
in Sections and
(Programs and ).

An algorithm to compute a geometric series summation using the closed-form expression (Equation ) is given in Program . This algorithm makes use of Program to compute .

**Program:** Program to compute using the closed-form expression

To determine the average running time of Program
we will make use of Equation ,
which gives the average running time for the `Power` function
which is called on line 5.
In this case, the arguments are *x* and *n*+1,
so the running time of the call to `Power` is
.
Adding to this the additional work done on line 5 gives
the average running time for Program :

The running times of the three programs
which compute the geometric series summation
presented in this chapter are tabulated below
in Table
and are plotted for in Figure .
Figure shows that,
according to our simplified model of the computer,
for *n**<*4, Program has the best running time.
However as *n* increases,
Program is clearly the fastest of the three
and Program is the slowest for all values of *n*.

**Figure:** Plot of Running Time vs. *n* for Programs , and

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.