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13 February, 14:35

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.

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  1. 13 February, 14:58
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    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
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