Question

Write a program to calculate and print the sum of odd numbers and the sum
of even numbers for the first n natural number. The integer n is to be entered
by the user

Answer 1

Answer:

The sum of the even numbers will be 2 ( 1 + 2 + 3 + … + n/2) if n is even.

= 2 (n/2) (n/2 +1) / 2

= n^2 / 4 + n/2 or you prefer n/2 (n/2 + 1). (****)

Check to see if it works.

The sum of the even numbers for the first 6 natural numbers is 2+4+6 = 12

and 3 (3+1) = 12. It seems to work.

The sum of the even numbers will be 2 (1 + 2 + 3 +…+ ((n+1)/2) if n is odd.

= 2 (((n-1)/2 ) ((n-3)/2)))

= (n-1) ( n-3)/2. (****)

Check to see if it works.

The sum of the even numbers for the first 9 natural numbers is 2+4+6+8= 20

and (8)(5)/2 = 20. Again it seems to work.

The sum of the odd numbers will always be a perfect square. It will be (n/2)^2 if n is even

= n^2 / 4. (****)

Check to see if it works.

The sum of the odd numbers for the first 8 natural numbers is 1+3+5+7=16

and 8^2 / 4 = 16. It seems to work.

The sum of the odd numbers will always be a perfect square. It will be ((n + 1) / 2)^2 if n if odd.

= (n + 1)^2 / 4. (****)

Check to see if it works.

The sum of the odd numbers for the first 11 natural numbers is 1+3+5+7+9+11=36

and 12^2 / 4 = 144/4 = 36.

Answer 2

Question:

Write a program to calculate and print the sum of odd numbers and the sum of even numbers for the first n natural numbers. The integer n is to be entered by the user.

Solution:

Language used : Java

import java.util.*;

public class OddEven

{

static void main()

{

Scanner sc=new Scanner(System.in);

int i,n,s1=0,s2=0;

System.out.println("Enter a number:");

n=sc.nextInt();

for(i=1;i<=n;i++)

{

if(i%2==0)

s1=s1+i;

else

s2=s2+i;

}

System.out.println("Sum of even numbers="+s1);

System.out.println("Sum of odd numbers="+s2);

}

}