Show That the Series $\frac{1}{n}+ \frac{1}{n+1} +\dots + \frac{1}{2n}$ Converges to a Number Between $\frac{1}{2}$ and $1$
How do I prove that the limit of the sequence exists: $a_n = \frac1n +\frac 1{n+1} + \frac1{n+2} + \dots + \frac1{2n}$?