Find the number of terms and the sum of the geometric series below.

$\displaystyle x+x^3+x^5+...+x^25$

Answer:

$\displaystyle n=13$

$\displaystyle S_{13}=\frac{x(1-x^{26})}{1-x^2}$

Why the answer given is

$\displaystyle S_{13}=\frac{x(1-x^{26})}{1-x^2}$

but not

$\displaystyle S_{13}=\frac{x(x^{26}-1)}{x^2-1}$

?