Using the Design Recipe, write the algorithm (not the program) for the following problems:
Write a program that prints the sum of the first n positive integers, 1 + 2 + ... + n, where n is user-specified.
Write a program that prints the product of the first n positive integers, 1 × 2 × ... × n, where n is user-specified.
Write a program that prints the balance of an account after each of a number of years y, given an initial balance b and a yearly interest i, specified as a percentage (e.g., 5%). The values of y, b and i are all user-specified.