Exercises

After completing the tutorial attempt the following exercises.

If you are not sure how to do something, have a look at the “How To” section.

1. Write a function that generates \(n!\).

2. Write a function that generates the \(n\)th triangular numbers defined by:

   \[ T_n = \frac{n(n+1)}{2} \]

3. Verify the following that the following identify holds for positive integer values \(n\leq 500\):

   \[ \sum_{i=0}^n T_i = \frac{n(n+1)(n+2)}{6} \]

4. Consider the Monty Hall problem:

   1. Write a function that simulates the play of the game when you ‘stick’ with the initial choice. You might find random.shuffle and poping a list helpful.

   2. Write a function that simulates the play of the game when you ‘change’ your choice. You might find removeing from a list helpful.

   3. Repeat the play of the game using both those functions and compare the probability of winning.