C++ Program

Description: The assignment for this week is proposing to practice your skills in solving problems using recursion, by identifying the base case and the recurrence relation to implement recursion functions that correctly solving three examples of algebraic series commonly used in Discrete Math. You will write a C++ drive program that implements a recursive function to solve each one of these algebraic series indicated in the bottom (I, II and III), each recursion function will receive an N integer number to calculate the N-th number of the series. Your program will request from the user to input a positive integer number N and then display the N-th number calculated for each series (I, II and III). Make sure that your drive program provides the user with a suitable interface for input, output, and an option to exit the program. The series your program will implement as recursive functions are: I. Padovan Sequence - P(n): It is a sequence of natural numbers that follow the pattern below. Some numbers that compose this sequence are : 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28 ... More about the Padovan Sequence can be found here (https://en.wikipedia.org/wiki/Padovan_sequence and http://mathworld.wolfram.com/PadovanSequence.html) II. Pell Numbers - p(n): It is a sequence of positive integer numbers that follow the pattern below. Some numbers that compose this sequence are : 0, 1, 2, 5, 12, 29, 70, 169, 408, 985 ... You can find more about the Pell numbers here (https://en.wikipedia.org/wiki/Pell_number and http://mathworld.wolfram.com/PellNumber.html) III. Catalan Numbers - C(n): It is a sequence of numbers that follow the pattern below. Some numbers that compose this sequence are : 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786 ... You can find more about the Catalan numbers here (https://en.wikipedia.org/wiki/Catalan_number and http://mathworld.wolfram.com/CatalanNumber.html)