Discrete Time Convolution Evaluation
The multiplication of the two unit step sequences $u[k]\cdot u[-n+k-1]$ is only non-zero if both sequences are non-zero. This means that the condition $k\ge 0$ as well as the condition $k\ge n+1$ must be satisfied. So you have two cases: for $n&lt;=-1$ you have to evaluate the sum with the lower limit $k=0$, and for $n&gt;-1$, you have to evaluate the sum with a lower limit $k=n+1$.