Correlation of discrete time periodic sequences So I was reading this textbook -  Digital Signal Processing by Proakis and Manolakis. The authors define the cross-correlation operation for 2 energy signals $x(n)$ and $y(n)$ in section 2.6.1 as:

$$ r_{xy}(l)=\sum_{n=-\infty}^{\infty}x(n)y(n-l) $$

In section 2.6.3, they define the cross-correlation operation of two power signals as:

$$ r_{xy}(l)=\lim_{M\to\infty}\frac{1}{2M+1}\sum_{n=-M}^{M}x(n)y(n-l) $$

My question is, why do we need to have a separate definition for power signals? Are these two definitions the same? If they aren't same, what is the intuition behind defining them like that?
Energy signals (such as an exponentially decaying pulse) are bounded in total energy as time goes to infinity in which case you can use the first definition. Power signals (such as a sine wave) have finite energy over finite time intervals but infinite energy for all time (power is energy/time) so the first equation will not converge in that case.