I answered a question in my probability test but I think it's wrong!
Could you tell me with my solution is right? The question is:
Find $$\lim_{n\to\infty}\int_{2n}^\infty\frac{1}{2^n(n-1)!}t^{n-1}e^{-t/2}dt$$
My solution:
This is the limit of survival function of a random variable $X\sim \Gamma(n,1/2)$ or a $X\sim \chi_{(2n)}^2$. That's it $S_x(2n)$.
$$\lim_{n\to\infty}S_x(2n)=0$$
It this correct?