I was trying to convolve two discrete sequences $x[n] = (-3)^n u(-n-1)$ with $h(n)=(\frac{1}{2})^n u[n+2] $ and was wondering if the work can be completed without having to plot the graph of the functions to find the limits of my summation formula (Completely analytic solution).
I reached a place in the summation where I got $$\sum _{i=-\infty} ^{i=+\infty} (-3)^i u(-i-1) \bigg( \frac{1}{2}\bigg)^{n-i} u(n-i+2) $$
can I know the limits from here?
I thought about $u(-i-1)>0$ then $i<-1$ and $u(n-i+2)>0$ then $i<n+2$ but is this of any use?