Consider a mathematical series such that the number Sn with index n (with n > 0) is defined as follows: n Sn = { 2 = 1 +2 + 22 + 2 + ... + 2" i=0 The sequence of numbers in this series is therefore 1, 3, 7, 15, 31, 63, 127, ... (i) Using iteration as the principal methodology, write a function that calculates the number Snin the series for a given index n. The function should take an integer n as input and return an integer. In your answer, use either pseudo- code or C code to describe the function. (ii) Write a second function that calculates the number Sn in the series for a given index n using recursion this time. The function should again take an integer n as input and return an integer. In your answer, use either pseudo-code or C code to describe the function. (iv) Write a third function that calculates in constant time, i.e. with computational complexity 0(1), the number Sn in the series for a given index n. The function should again take an integer n as input and return an integer. In your answer, use either pseudo-code or C code to describe the function