Finding the stability of the system Determine whether the system $h(n)=nu(n)$ is BIBO stable or not.

I have solved it and got it as unstable as $\displaystyle\sum_{n=-\infty}^\infty \lvert h(n)\rvert = \infty$. But the book ¹ is saying stable:

Which one is correct?

¹: S. Poornachandra, B. Sasikala: Digital Signal Processing. Third Ed. McGraw Hill, New Delhi
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.