I have to find a convolution of two signals
$h[n] = 0.5^nu[n]$
$x[n] = u[n]-u[n-3]$
the final sum, which is correct is:
$$\sum_{m=n-2}^n 0.5^mu[m] $$
note that i replaced $n-k$ with $m$, that is $ m = n-k $
So, in regards to parameter $n$, I have to decypher the formula. The result is:
$$ \begin{array}{lr} 0, & n < 0 \\ 2 \cdot (1-0.5^{n} \cdot 0.5), & 0 \le n \lt 2 \\ 1.75 \cdot 0.5^{n} / 0.5^{2}, & n \ge 2 \end{array} $$
But, i don't know how to get those results. Can you please explain?
The results are correct (maybe i just typed something wrong, if that's the case, I'm sorry in advance)
I'm having trouble with the sums, so I'm guessing this is more appropriate for the math.stackexchange than dsp.stackexchange.