$$x[n] = u[n]+u[-n]$$
Is it periodic or not? My answer is
$$u[n] = {1 , n\geqslant0}$$
$$u[-n] = {1 , n\leqslant0}$$
which means that the signal $x[n]$ is always equal to $1$ from $-\infty$ to $+\infty$, but it equals $2$ at $n=0$. Am I right?