In the context of the proof of Theorem 4.20, use Theorem A. 22 to prove that \(\left[1-\frac{1}{2} n^{-1} t^{2}+o\left(n^{-1}ight)ight]^{n}=\left[1-\frac{1}{2} n^{-1} t^{2}ight]+o\left(n^{-1}ight)\) as \(n ightarrow \infty\) for fixed \(t\).

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1 Theorem 4.20 (Lindeberg and Lvy). Let {X} be a sequence of inde- pendent and identically distributed random variables such that E(X) = and V(X) = 0 < for all n = N, then Z = n(Xn - ) Z as n o where Z has a N(0, 1) distribution.