So if I wanted to rewrite this, I'm just going to rewrite it to make it a little bit simpler. So the expected, at least for the purposes of this proof, so the expected value of X is equal to, I'll write this as one P plus two P times one minus P plus three P times one minus P squared. And we're going to keep going on and on and on forever like that. So how do we figure out this sum? Well now I'm going to do a little bit of mathematical trickery or gymnastics, but it's all valid. And if any of y'all have seen the proof of taking a infinite geometric series, then we're going to do a very similar technique. What I'm going to do here is I'm going to think about well what is one minus P times this expected value?