1. The problem statement, all variables and given/known data Two questions lim as n -> infinity (1^k + 2^k + ... + n^k) / n^(k+1) and lim as n -> infinity 1/(n+1) + 1/(n+2) + ... + 1/2n 2. Relevant equations Definitions of limits, laws of exponents etc. 3. The attempt at a solution Well I think I have them both solved but it seems too easy therefore I think I did something wrong or am missing something. I think they are both zero. The first one you can rewrite the term in the limit as (1^k)/(n^(k+1)) + ... + (n^k)/(n^(k+1)) If you take the limit as n goes to infinity of each of these, then they all go to zero. I am not quite sure I can do this, or argue this that way, but it is the only thing that comes to mind. For the second question, I do the same thing. Take the limit as n goes to infinity of each term. Since they all go to 0 the entire limit goes to zero. Please let me know if my reasoning is correct.