Question

Given that n refers to a positive integer, use a while loop to compute the sum of the cubes of the first n counting numbers, and associate this value with total. Use no variables other than n, k, and total.

Answer 1

Answer:

int k = 1;

int total = 0;

while (k <= n){

  total = total + (k*k*k);

  k++;

}

Explanation:

The code above has been written in Java.

Following is the line-by-line explanation of the code written as comments.

// Initialize int variable k to 1.

// variable k is used to control the loop.

// It is initialized to 1 because the positive integers should start at 1.

// Starting at zero will be unimportant since the cube of 0 is still zero and

// has no effect on the overall sum of the cubes.

int k = 1;

// Initialize total to zero(0)

// This is so because, at the start of the addition total has no value.

// So giving it zero allows to cumulatively add other values to it.

// Variable total is also of type int because the sum of the cubes of counting

// numbers (which are positive integers) will also be an integer

int total = 0;

// Now create a while loop to repeatedly compute the sum of the cubes

// while incrementing the counter variable k.

// The condition for the loop to execute is when k is less than or equal to

// the value of variable n.

// The cube of any variable k is given by $k^{3}$ which can be

// written as k * k * k.

// At every cycle of the loop, the cube of the counter k is calculated and

// added cumulatively to the value of total. The result is still stored in the

// variable total. After which k is incremented by 1 (k++).

while (k <= n) {

  total = total + (k*k*k);

  k++;

}