Limit of chi-square tail probabilities

Let $\{X_n\}_{n\ge1}$ be a sequence of independent random variables with $X_n$ having the probability density function

$$f_n(x)=\begin{cases}\dfrac1{2^{n/2}\Gamma\left(\frac n2\right)}e^{-\frac x2}x^{\left(\frac n2-1\right)}, & x>0,\ 0, & \text{otherwise.}\end{cases}$$

Then $\lim_{n\to\infty}\left[P\left(X_n>\dfrac34n\right)+P\left(X_n>n+2\sqrt{2n}\right)\right]$ equals