Easy Haskell coding question

1. Write a recursive method to compute m(i) = 1 + 1/2 + 1/3, ... + 1/i, where i is an Int

2. Write a recursive method to compute m(i) = 1/2, 2/3, ... i/(i + 1), where i is an Int

3. Using recursion, implement a method that removes the max element from a list of Ints, or one of the max elements if there is more than one. E.g., [1,2,3,3,4] should become [1,2,3,4]

4. Implement a sorting algorithm that finds the max, puts it at the end of the list, then recursively sorts the remainder of the list. You can create/use any helper functions you need, provide that you wrote it yourself, or it's built into Haskell.

Please use computer to write the code.

Include type definitions for all functions.