Ononot — For i.i.d. random variables X1, X2, \dots, Xn with E[Xi] = 0

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Random Variableshard

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For i.i.d. random variables $X_1, X_2, \dots, X_n$ with $E[X_i] = 0$ and $E[X_i^2] = 1$ , what is the limit of the moment generating function of $S_n = \frac{1}{\sqrt{n}} \sum_{i=1}^n X_i$ as $n \to \infty$ ?