Calculating the limit of $\lim\limits_{n \to \infty} (\frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + ...+\frac{1}{2n})$ Hello everyone how can I calculate the limit of:
$\lim\limits_{n \to \infty} (\frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + ...+\frac{1}{2n})$

Hint:
Factor out $n$ in all denominators:
$$\frac{1}{n+1} + \frac{1}{n+2}  + …+\frac{1}{2n}=\frac1n\biggl(\frac1{1+\frac1n}+\frac1{1+\frac2n}\dots+\frac1{1+\frac nn}\biggr)$$
and recognise a Riemann sum.
