rational function limit involving factorials I posted something similar but someone edited the question and added the wrong equation, which gave irrelevant responses. 

Lim (2n-1)!/(2n)^n as n approach infinity. 

Any method, I would just like a starting, no full answer needed (but will be appreciated)!
Hint. You may recall the Stirling formula
$$
n!\sim\sqrt{2\pi n}\left(\dfrac{n}{e}\right)^n
$$ as $n$ is great, giving
$$
\frac{(2n-1)!}{(2n)^n}\sim\sqrt{2\pi (2n-1)}\left(\dfrac{2n-1}{e}\right)^{2n-1}\frac{1}{(2n)^n} \sim\frac{\sqrt{2\pi}}{e}\left(\dfrac{2n}{e^2}\right)^{n-1/2} 
$$
then your limit is $+\infty$ since $\displaystyle \dfrac{2n}{e^2} \longrightarrow +\infty$.
Use  the formula $|a_{n+1} / a_n|$