I would start with part b), which you are told to prove by induction. The base case is easy to check, so what about the inductive step? We are told that , which you can simplify to (check that!).
If then , which simplifies to . That completes the inductive step.
Once you have done part b), you should be able to work out the limit of t_n as n→∞. That will deal with part a) and also help towards part c).