How to derive the closed form solution of geometric series I have the following equation: 
$$g(n) = 1 + c^2 + c^3 + ... + c^n$$ 
The closed form solution of this series is $$g(n) = \frac{c^{n+1} -1}{c-1}$$
However, I am having a difficult time seeing the pattern that leads to this.
$$ n =0 : 1 $$ $$ n =1 : 1 + c $$ $$ n = 2 : 1 + c + c^2 = 1 + c(1+c)$$ $$ n =3 : 1 + c(1+ c(1 + c))$$
Can someone provide some insight here?

Let $S=1+c+c^2+...+c^n$ then $c.S=c+c^2+...c^{n+1}$, subtract them.
