I'm stuck on the following problem from Rudin:

we're given: .

The first question was to prove that if . This was easy to prove if we let and then integrate by parts.

The second question is to show that where where c is a constant. Well, that was also easy to prove and we get c = 2.

Now, the third parts asks for the upper and lower limits of as . How can we do this?

Finally, we're asked whether converges or not. How can we know?

Thank you in advance.