Overview: There are in fact many applications of series, unfortunately most of them are beyond the scope of this course. One application of power series is in the field of Ordinary Differential Equations when finding Series Solutions to Differential Equations. Another application of series arises in the study of Partial Differential Equa- tions. One of the more commonly used methods in that subject makes use of Fourier Series. Many of the applications of series, especially those in the differential equations fields, rely on the fact that functions can be represented as a series. In these applications it is very challenging, if not impossible, to find the function itself. However, there are methods of determining the series representation for the unknown function. While the differential equations applications are beyond the scope of this course there are some applications from a Calculus setting and in this project we wll look at two of them Problem 1 (Application of Geometric Series) A ball was dropped from a height of 5 feet and begins boung. The height of each bounce is three-fourths the height of the previous bounce. Thus aftertheb hits the floor for the first time, the ball rises to a height of 5( 3.75 feet, and after it hits the floor for the second tine, the ball rises to a height of 3.75( = 5ã©a_ 2.8125 feet. (1) Find an expression for the height to which the ball rises after it hits the floor for the nh time