10. Palindrome Check A number is called a palindrome if it remains unchanged when its digits are reversed. Write a program to accept a nonzero positive number. The program should loop till the user inputs a valid number. The program should then generate the reversed num- ber. If the reversed number is equal to the original, a message should be displayed that the number is a palindrome. Hint: To find the reverse of a number, you can follow this procedure to reverse a number n. Initialize reversed number revno to 0. Divide n by 10 and store the remain- der in r. Then add the remainder r to revno multiplied by 10. Repeat continually until n becomes 0. 13. Sum of a Series Write a program that displays the following series and also finds its sum: 2 4 6 8 10 20 + + + 12 22 42 102 + + + 32 52 24. Using Files-Numeric Processing If you have downloaded this book's source code from the Computer Science Portal, you will find a file named Random.txt in the Chapter 05 folder. (The Portal can be found at www.pearsonglobaleditions.com/gaddis.) This file contains a long list of ran- dom numbers. Copy the file to your system, then write a program that opens the file, reads all the numbers from the file, and calculates the following: A) The number of numbers in the file B) The sum of all the numbers in the file (a running total) C) The average of all the numbers in the file The program should display the number of numbers found in the file, the sum of the numbers, and the average of the numbers