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:

   $$3n^3-183n^2+3318n-18757$$

   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?