Why in formula of power of periodic signal is $2N+1$?
Isn't $-N$ to $N$ $2N+1$ index in total (you probably missed the 0 here)
$$ P = \lim_{N\to\infty} {\frac{1}{2N+1} \sum_{n=-N}^N} \lvert x[n] \rvert^2 $$