Write Java programs with loops that compute:a. The sum of all even numbers between 2 and 100 (inclusive).

b. The sum of all squares between 1 and 100 (inclusive).

c. All powers of 2 from 20 up to 220.

d. The sum of all odd numbers between a and b (inclusive), where a and b are inputs.

e. The sum of all odd digits of an input. (For example, if the input is 32677, the sum would be .)

a.The sum of all even numbers between 2 and 100 (inclusive).

public class SumofEvenNumbers

{ public static void main(String[] args) {

  int sum=0; // stores the sum of even numbers

/* loop starts from 2 and terminates when value of i becomes greater than 100 At each iteration the value of i is incremented by 2 and added to the sum variable to add the even numbers */

for(int i=2; i<=100; i+=2){

 sum = sum + i;}  

System.out.println("Sum of all even numbers between 2 and 100 (inclusive) is " + sum);} }

//displays the sum of even nos from 2 to 100

Output:

Sum of all even numbers between 2 and 100 (inclusive) is 2550

b. The sum of all squares between 1 and 100 (inclusive).  

Sum of square from 1 to 100 is 1+4+9+16+25+36+49+64+81+100

public class SumofSquares

{ public static void main(String[] args) {

int square;

int sum = 0;

for(int i = 1; i<=10; i++) {

   square= (i*i);

   sum += square; }

System.out.println("The sum of all squares between 1 and 100 (inclusive) is " + sum);}}

Output:

The sum of all squares between 1 and 100 (inclusive) is 385

c. All powers of 2 from 2^0 up to 2^20.      

The program if you want to display all the the powers of 2 from 2^0 to 2^20:

import java.lang.Math;

public class Powers

{public static void main(String[] args) {

   double  power = 0; // stores the powers

       for(int i = 0; i <= 20; i++) // loop starts from i=0 and terminates at i>20

           {power = Math.pow(2, i); // computes power of 2 from 2^0 to 2^20

     System.out.println("2 ^ " + i + " = " + (int) power);}

//displays all powers of 2 by converting each power of 2 to integer

}}

Output:

2 ^ 0 = 1                                                                                                    

2 ^ 1 = 2                                                                                                                    

2 ^ 2 = 4                                                                                                                  

2 ^ 3 = 8                                                                                                                  

2 ^ 4 = 16                                                                                                                  

2 ^ 5 = 32                                                                                                                

2 ^ 6 = 64                                                                                                                

2 ^ 7 = 128                                                                                                                

2 ^ 8 = 256                                                                                                              

2 ^ 9 = 512                                                                                                              

2 ^ 10 = 1024                                                                                                            

2 ^ 11 = 2048                                                                                                            

2 ^ 12 = 4096                                                                                                          

2 ^ 13 = 8192                                                                                                            

2 ^ 14 = 16384                                                                                                          

2 ^ 15 = 32768                                                                                                        

2 ^ 16 = 65536                                                                                                        

2 ^ 17 = 131072                                                                                                        

2 ^ 18 = 262144                                                                                                      

2 ^ 19 = 524288                                                                                                      

2 ^ 20 = 1048576

The following program is to find the sum of all powers of 2 from 2^0 to 2^20

import java.lang.Math;

public class Powers

{public static void main(String[] args) {

   double  power = 0;

   double sum=0;

       for(int i = 0; i <= 20; i++){

          power = Math.pow(2, i);// calculates all powers of 2 from 2^0 to 2^20

          sum = sum + power;} // calculates sum of all powers from 2^0 to 2^20

       System.out.println("sum of all powers of 2 from 2^0 to 2^20 is " + sum);}}

Output:

sum of all powers of 2 from 2^0 to 2^20 is 2097151.0

d. The sum of all odd numbers between a and b (inclusive), where a and b are inputs.

import java.util.Scanner; //to take input from user

public class SumOddNumbers

{public static void main(String[] args) { // main() function body

Scanner input = new Scanner(System.in); //create object of Scanner class

      System.out.print("Enter two numbers: ");

//prompts user to enter two numbers

      int a = input.nextInt();  // scans and reads first number input by user

      int b = input.nextInt();//scans and reads 2nd number entered by user

      int sum = 0; // stores the sum of odd numbers

/* loop starts from i = a which is the first input number and continues till the value of i gets greater than b which is the 2nd input number */

      for (int i = a; i <= b; i++)       {

          if (i % 2 == 1) //checks if the number in the range a to b is odd

            sum += i;       } // adds the odd numbers

      System.out.println("The sum of all odd numbers between " + a + " and "+ b + " (inclusive) is " + sum); }}

// displays sum of odd numbers in the given range

Output:

The sum of all odd numbers between 1 and 10 (inclusive) is 25      

e. The sum of all odd digits of an input.      

import java.util.Scanner;  // to take input from user

public class SumOfOddDigits

{public static void main(String[] args) { // main() function body

Scanner input = new Scanner(System.in); // create object of class Scanner

//prompts user to enter a number

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

//scans and reads numbers from user

   int number = input.nextInt();

   int sum=0; //stores the sum of odd digits of input number

   while(number>0){

// loop executes till value of number variable is greater than 0

     int remainder = number % 10;

/*takes mode of input number to calculate the remainder of the number, this means each digit of the number is separated. For example if the number is 32677 then after taking mod we get 7 in first iteration */

     if(remainder % 2!=0){

/*checks if the value in remainder is odd which means the digit is not completely divisible by 2 and the mod of the digit with 2 is not equal to 0 */

       sum = sum + remainder;      } // adds the odd digits of input number

     number = number / 10;    }

// divides the number by 10 for example 32677/10 is 3267 in first iteration

   System.out.println("sum of all odd digits is " + sum); }}  

// displays sum of the odd digits of input number    

Output:        

Enter a number:                                                                                                    

32677                                                                                                                    

sum of all odd digits is 17  

answer; geometric center line;