Don’t forget to push your answers to your remote repository by the end of quiz time. Push all your answers to quiz/3/ folder in your Github project.

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

$$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots = \sum^{\infty}_{n=0} \frac{1}{2^n} ~,$$

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

$$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots + \frac{1}{2^m} = \sum^{m}_{n=0} \frac{1}{2^n} ~,$$

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.