Finding the stability of the system
That's a (copy-paste) mistake in the book. The result in the given example is that the sum doesn't converge, yet the author concludes that the system is stable, which is obviously wrong:

$$\sum_{n=-\infty}^{\infty}|h[n]|=\sum_{n=0}^{\infty}n=\infty$$

The system is not BIBO-stable.