1) Write a program that computes

4\cdot \sum_{k=1}^{10^6} \frac{(-1)^{k+1}}{2k-1} = 4\cdot(1-1/3+1/5-1/7+1/9-1/11\ldots).

and

also how to do this by the method asked in the question;

2) Write a function that rotates a list by k elements. For example [1,2,3,4,5,6] rotated by two becomes [3,4,5,6,1,2]. Try solving this without creating a copy of the list. How many swap or move operations do you need?

these both questions are from https://adriann.github.io/programming_problems.html