Prove Algebric Identity 
Possible Duplicate:
Value of $\sum\limits_n x^n$ 

Given $a\in\mathbb{R}$ and $0<a<1$
let $(X_n)$ be a sequence defined: $X_n=1+a+a^2+...+a^n$,  $\forall n\in\mathbb{N}$.
How do I show that $X_n=\frac{1-a^{n+1}}{1-a}$
Thanks.

$$\begin{align*}
(1-a)(1+a+a^2+\dots+a^n)&=(1+a+\dots+a^n)-a(1+a++\dots+a^n)\\
&=(1+\color{red}{a+\dots+a^n})-(\color{red}{a+a^2++\dots+a^n}+a^{n+1})\\
&=1-a^{n+1}
\end{align*}$$
