Is there a way to convert $\sum_{n=0}^{i-2}\frac{1}{2^n}$ summation to a closed form?

Question

Is the geometric series applicable here? I thought no since the raised power would be negative, but I don't see another way to convert it.

Thanks!

Answer 1

Geometric series has $$ \sum_{k=0}^N a^k = \frac{a^{N+1}-1}{a-1}, \quad \forall a \in \mathbb{R}, N \in \mathbb{N}. $$

In your case, plug in $a = 1/2$ and $N = i-2$...