Given the infinite series$\displaystyle \sum_{r=0} ^\infty\left ( \frac{1-x}{x} \right )^r$

a)show that the series is a geometric series

b)determine the set of value of $\displaystyle x(x>0)$ so that the sum to infinity ,$\displaystyle S_{\infty}$ exist

c)if $\displaystyle x = 2$, find the sum of the first five terms,$\displaystyle S_5$ and $\displaystyle S_{\infty}$.Show that $\displaystyle S_5 : S_{\infty} = 33:32$