formula derivation for periodic signal power

Studying DSP on my own. Taking an introductory class. Was given a formula for signal power

$$P = \lim_{M\to\infty} {\frac{1}{2M+1} \sum_{n=-M}^M} \lvert x[n] \rvert^2$$

I do understand why the formula looks the way it does.

But then we were given a formula for a power of a periodic signal, where $N$ is the period,

$$P = {\frac{1}{N} \sum_{n=0}^{N-1}} \lvert x[n] \rvert^2$$

I can't figure out how this formula is derived from the original one. How do I do it?