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. Using a for loop print the types of the variables in each of the following iterables:

   1. iterable = (1, 2, 3, 4)

   2. iterable = (1, 2.0, 3, 4.0)

   3. iterable = (1, "dog", 0, 3, 4.0)

2. Consider the following polynomial:

   \[ 3 n ^ 3 - 183n ^ 2 + 3318n - 18757 \]

   1. Use the sympy.isprime function to find the lowest positive integer value of \(n\) for which the absolute value of that polynomial is not prime?

   2. How many unique primes up until the first non prime value are there? (Hint: the set tool might prove useful here.)

3. Check the following identify for each value of \(n\in\{0, 10, 100, 2000\}\):

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

4. Check the following identify for all positive integer values of \(n\) less than 5000:

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

5. Repeat the experiment of selecting a random integer between 0 and 10 until it is even 1000 times (see Repeat code while a given condition holds). What is the average number of times taken to select an even number?