Limit of a probability for a sum of uniform variables

Let $X_1,X_2,…$ be a sequence of i.i.d. $U[0,1]$ random variables. If $Y_n=\sum_{i=1}^nX_i$, $n=1,2,…$, then $\lim_{n\to\infty}P\left(Y_n\le\frac n2+\sqrt{\frac n{12}}\right)=$