Extra practice with ``while`` loops
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1. Write a function ``oddsum(n)`` that will return the sum of all odd numbers from ``1`` to ``n``.
2. Modify ``oddsum`` so that it takes *two* parameters: ``oddsum(n,m)`` and returns the sum of all odd numbers from ``n`` to ``m``.
3. Write a function that will return the sum of all even numbers from ``1`` to ``n`` *plus* the product of all odd numbers from ``1`` to ``n``.
   (viz., add up all the even numbers between 1 and n, multiply together all the odd numbers between 1 and then add those two values).

4. Write a function that computes the value of the following mathematical expression :math:`\sum_{i=1}^n x \cdot \frac{1-x^n}{1-x}`.
   The function will take two parameters: ``n`` and ``x``.
5. Write a function that computes the value of the following mathematical expression :math:`\sum_{i=0}^n \frac{x^i}{i!}`. Remember
   that ``!`` denotes the _factorial_ function (which you've already seen as the ``dostuff`` function in Lecture #6).
6. Write a function ``isprime(n)`` that returns ``True`` if ``n`` is prime and ``False`` otherwise. Remember that a number
   is prime if it is divisible by 1 and itself and *nothing else*.
7. Write a function ``primes_less_than(p)`` that will print out all of the prime numbers (greater than 1 and) less than ``p``.
8. Write a function ``rand_loop(cutoff)`` that will return a count of how many times the interpreter makes it through a special loop. The loop
   condition will be the following expression ``numpy.random.rand() < cutoff``. You will need to ``import numpy`` in
   your code. The ``random.rand()`` function generates a random number between 0 and 1, so the function parameter ``cutoff`` should
   be a floating point value between 0 and 1. In short: your function will generate a random number. If it's less than the cutoff
   you'll increment a counter and go through the loop again. If it's equal to, or bigger than, the cutoff, you stop looping and
   return the count. Play with the function a bit to find a relationship between your choice of cutoff and the number of times
   your function makes it through the loop.
9. Write a function ``mult_table(n)`` that will print out an :math:`n \times n` multiplication table for the values ``1`` to ``n``.
   *Hint*: you can *nest* ``if`` statements... can you nest ``while`` loops?