Question

Give a recursive algorithm to compute the sum of the cubes of the first n positive integers. The input to the algorithm is a positive integer n. The output is ∑j=1nj3. The algorithm should be recursive, it should not compute the sum using a closed form expression or a loop.

Answer 1

Answer:

def sum_cubes(n):

   if n == 1:

       return 1

   else:

       return n * n * n + sum_cubes(n-1)

print(sum_cubes(3))

Explanation:

Create a function called sum_cubes that takes one parameter, n

If n is equal to 1, return 1. Otherwise, calculate the cube of n, and add it to the sum_cubes function with parameter n-1

If we want to calculate the cubes of the first 3 numbers:

sum_cubes(3) = 3*3*3 + sum_cubes(2)

sum_cubes(2) = 2*2*2 + sum_cubes(1)

sum_cubes(1) = 1

If you substitute the values from the bottom, you get 27+8+1 = 36