These summation laws/formulas are used. They are very common and thus we won’t prove any of them. Most of them can be found here.
\(\displaystyle\sum_{n=s}^t C\cdot f(n) = C\cdot \sum_{n=s}^t f(n)\)
\(\displaystyle\sum_{i = 0}^{n-1} a^i = \frac{1 - a^n}{1 - a}\)