Okay, I've got this example in my notes and I don't understand it. My notes say...

Find $\displaystyle \sum_{k=0}^{\infty}3^{-k}$.

Step 1Find $\displaystyle S_{1}$, $\displaystyle S_{2}$...

Step 2Find the limit.

$\displaystyle S_{1}=\frac{1}{1\times2}=1-\frac{1}{2}$

But I don't understand that last bit. I know it's true (obviously) but why write it like that?