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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:

solution from book

Which one is correct?


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

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  • $\begingroup$ Which book? Can you add a scan of that example (and its answer) to the question? $\endgroup$ – Matt L. Sep 3 '16 at 11:39
  • $\begingroup$ books.google.com.np/… 59 qno.4) $\endgroup$ – Aneil Sep 3 '16 at 11:45
  • $\begingroup$ The solution from the book contradicts itself, and proves it's unstable. Just a typo. $\endgroup$ – Marcus Müller Sep 3 '16 at 15:11
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    $\begingroup$ I'm voting to close this question as off-topic because it's just based on a typo in the book, with the correct statement given directly above the typo. Hence, this question holds no value for future readers. $\endgroup$ – Marcus Müller Sep 3 '16 at 15:12
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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.

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