In part one, you can just compare terms directly. The -term in your first series is , and the -term in your second series is . Is it true that (for )? If so, then you have , and therefore, the first series is bounded by the second.
In part two, we can try to sum up the second series to put a bound on the first. Try writing it down using your hint:
Anything nice happen? What happens when you take ? Use this to conclude.