Intermediate Value Theorem

im supposed to use the IVT to prove that the equation

$\displaystyle g(x)= 1+x + \frac{x^2}{2}+....+\frac{x^{n-1}}{n-1}+\frac{x^n}{n}$ has at least one real solution. where $\displaystyle n$ is and odd positive integer and $\displaystyle g(x)=0$.

im not sure if when $\displaystyle n=3$ the equation looks like $\displaystyle g(x)=1+x+\frac{x^2}{2} + \frac{x^2}{2} + \frac{x^3}{3}$

or

$\displaystyle g(x)=1+x+\frac{x^2}{2}+\frac{x^3}{3}$

if its the second equation then i know that the intervals are $\displaystyle [-2,-1]$ because $\displaystyle g(-1)>g(-2)$