Power of a Discrete time signal
The power of a discrete-time signal $x[n]$ is given by

$$P_x=\lim_{N\rightarrow\infty}\frac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^2$$

which is identical to the first formula in your question. The second formula is wrong and does not even make any sense due to the infinite limits of the sum.

I'd advise you to use text books or high-quality internet resources such as MIT OpenCourseWare.