Does the series $\displaystyle \sum ^ \infty _{k=1} x^k $ on (0,1)? Pointwise or Uniformly?

Well, so far I have this:

Define the partial sum $\displaystyle S_n = \sum ^n _{k=1} x^k =1+x=x^2+...+x^n= \frac {1-x^{n+1}}{1-x}$

So the series converge point wise to $\displaystyle \frac {1}{1-x} $?