Explanation in a step of the summation $\frac{1}{2^n+1} + \frac{1}{2^n+2}+\cdots +\frac{1}{2^{n+1}}$ I have the solution to the above equation but I wanted to know the explanation for it.
$$\frac{1}{2^n+1} + \frac{1}{2^n+2}+\cdots +\frac{1}{2^{n+1}} = 2^n \frac{1}{  2^{n+1}}$$
and
$$2^n\frac{1}{2^{n+1}}=\frac{1}{2} \qquad \text{(I understand this part)}.$$
I wasn't sure how that became the product of those 2 numbers. Any explanation please? Thank you.
To make it clearer let me include this link:
https://www2.isye.gatech.edu/~hsharp/math2420/harmonic.pdf
Look at line 5
Im open to any alternative suggestions to solve the problem.

We have an inequality since $$\frac{1}{2^n+i}\geq \frac{1}{2^{n+1}}$$
for $1\leq i\leq 2^{n}.$ Thus $$\sum_{i=1}^{2^{n}}\frac{1}{2^n+i}\geq\sum_{i=1}^{2^n}\frac{1}{2^{n+1}}=\frac{1}{2^{n+1}}\sum_{i=1}^{2^n}1=2^n\frac{1}{2^{n+1}}$$
