Stability of the below function was asked.
$$ T(x[n]) = \sum_{k=n_0}^n x[n] $$
I understand that $x[n]$ shouldn't exceed $M$ value. $x[n]\le M$. I mean, we are looking for if the input is bounded, what will the output be.
However, i didn't understand from where $|n-n_0|M$ came from in the below function.
$$ \left |T(x[n]) \right| \le \sum_{k=n_0}^n \left| x[n] \right| \le |n-n_0|M $$