if we know  n! ~ \sqrt{2 \pi n}(\frac{n}{e})^n
as  n \rightarrow \infty
(i) define  r_{n} = \frac{\sqrt{n}}{n!}}(\frac{n}{e})^n
express log(\frac{r_{n+1}}{r_{n}})
(ii)prove that the following limit exists and calculate it
lim_{x \rightarrow 0} \frac{(1+x/2)log(1+x) -x}{x^3}