Hello!!!

I want to prove that at the field $\mathbb{Q}_p$, where $p$ is a prime, it stands:

$$-1=\sum_{0}^{\infty} (p-1)p^i$$

That's what I have tried so far:

$$-1=\sum_{i=0}^{\infty}(p-1)p^i =(p-1)+(p-1)p+(p-1)p^2+\dots \\ \Rightarrow 1-1=1+p-1+p^2-p+p^2-p^2+\dots \\ \Rightarrow 0=(1-1)+(p-p)+(p^2-p^2)+\dots$$

How can I continue?