Consider the following recursive algorithm for computing the sum of the first n cubes: S(n) = 1³ + 2³ + + n³.

(a) Set up a recurrence relation for the number of multiplications made by this algorithm.

(b) Provide an initial condition for the recurrence relation you develop at the question (a).

(c) Solve the recurrence relation of the question (a) and present the time complexity as described at the question number 1.

Algorithm S n) Input: A positive integer n Output: The sum of the first n cubes if n 1 return 1 else return S n 1) n n n