Section 13.9 Fun With Loops!

Write a program that prompts the user to enter a positive integer n and then computes the sum of the numbers from 1 through n. For example, if the user enters 5, then your program’s output should be:

A quick way to check that your program works is to ensure that the sum of the numbers from 1 to n equals \(\frac{n(n+1)}{2}\text{.}\)

Write two versions of this program: One using a while-loop, and another one using a for-loop.

Write a program that continuously asks the user to enter a nonzero number and adds up all of the numbers entered. The program should terminate when the user enters a zero and then print out the total sum.

Here is a sample run of the program:

Please enter a number: 5
Please enter a number: 11
Please enter a number: -3
Please enter a number: 0
The numbers you entered add up to 13.

Write a program that prompts the user for two numbers p and q, then calculates the greatest common divisor of p and q. You may do so using the "brute force" method: If q \(\leq\) p, for example, you simply check each of the divisors q, q-1, q-2, ..., 1, until you find one that divides both p and q.

Challenge: implement the Euclidean algorithm!

Write a program that determines whether a number entered by the user is prime (again, you may use the “brute force” method, going through all possible divisors 2, 3, 4, …, n).

(You only really need to check factors up to \(\sqrt{n}\text{.}\))