1.  A Geometric Series is defined by the following mathematical sequence,

A finite version of this sequence can be defined as the following,

a) Write a recursive function that takes an input integer m and computes the finite Geometric sum as defined above.

b) Write a non-recursive function, using loops, that takes an input integer m and computes the finite Geometric sum as defined above.

c) Write a third script, for example, named benchmark, that measures the speed of the above two function implementations for some input test value of m, and displays a message like the following,

Recursive implementation is 0.76 as fast as the loop-based implementation of the function.