# Summing a series with a changing power

$$\sum_{r=0}^{k-1}4^r$$
Hi, I was wondering whether anyone could explain how to work this out. I know the end result is $\frac{4^k-1}{3}$, but I don’t know why or how to get there.
Thank you 😀

#### Solutions Collecting From Web of "Summing a series with a changing power"

Multiply it by $(4-1)$. Expand without turning it into $4-1=3$. a lot of powers of $4$ will simplify except $4^k$ and $1$. Afterwards divide by $4-1=3$.