Question

14) Modify the method that calculates the sum of the integers between 1 and N. Have the new version match the following recursive definition: The sum of 1 to N is the sum of 1 to (N/2) plus the sum of (N/2 1) to N. Trace your solution using an N of 7.

Answer 1

Explanation:

Let solve the program using Java programming language

Method: method means group of statements to perform some operation.

             let call the method sum.

Parameters: list of variables that are use in the method for declaration.

The code

public int sum (int number)

int answer;

if (number == 1)

answer = number;

else

{

int half = number/2;

int span = number - half;

answer = sum(half) + sum(span) + (half * span);

}

answer result;

}

Firstly we defined the method called sum(), the method takes only one parameter which is number and return the answer(sum of  the integers 1 and N).

if the number is equal to 1, so it will return the number and if the number is not equal to 1 it will divide the number by 2 and get the span(span used to shift upper range).And result will add sum of half, sum of span and product of half span.