1+\frac{1}{2}+\frac{1}{3}+ ... +\frac{1}{2^{n}-1}+\frac{1}{n}+\frac{1}{2^{n}+1}+ ... +\frac{1}{2^{n+1}-1} > \frac{n}{2}+2^{n}*\frac{1}{2^{n+1}} = \frac{n}{2}+\frac{1}{2} = \frac{n+1}{2}