Chapter 1.6, Problem 2P

Prove that the harmonic series ${\displaystyle {\sum }_{n=1}^{\infty }1/n}$ is divergent by comparing it with series $\begin{array}{l}1+\frac{1}{2}+\left(\frac{1}{4}+\frac{1}{4}\right)+\left(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\right)+\left(8\text{terms}\text{each}\text{equal}\text{to}\frac{1}{16}\right)+\mathrm{....},\\ \text{which}\text{is}1+\frac{1}{2}+\frac{1}{2}\text{}+\frac{1}{2}+\frac{1}{2}+\mathrm{...}\end{array}$