Calculating a periodic signal (way of solving this)?

Question

I created my own examples so i can have the gist of how to solve the real ones that my homework needs so here we go:

$$x(t)=\sum_{n=-\infty}^\infty \Pi\left({t-4n\over2}\right) + \sum_{n=-\infty}^\infty Π{(t-4n)} $$

So i want to find if this singal is periodic and what it's period, can i have a step by step solution (more like understanding)?

What concernes me is how i tackle the sums.

Answer 1

HINT: Let be $f(t)=\Pi(t/2)+\Pi(t)$. So we have $$ x(t)=\sum_{n=-\infty}^\infty f(t-4n) $$ Can you see that $x(t)$ is periodic with period $T=4$?