Why add one to denominator when calculating discrete signal average power?

Question

In order to calculate the average power of a continuous signal we use the following formula:

Which makes logical sense to me. However, when we're calculating it for a discrete signal, then we use the following formula:

My question, and confusion, is why we add one to the divisor of the summing co-efficient?

Answer 1

The number of integers in interval $[n_0, n_1]$ is equal to $n_1-n_0+1$.

Example. Let's count the number of integers from $n_0=3$ to $n_1=7$: $$3\le n\le7\qquad \{3,4,5,6,7\}\qquad\text{5 integers total}$$ $$n_1-n_0+1=7-3+1=5$$