Central Limit (distribution of scaled random walk)

Question

I have been reading Steven E Shreve's Stochastic Calculus for Finance Volume II Continuous-time models. I'm trying to understand a theorem from Chapter 3 that says that distribution of scaled random walk $W^{n}(t)$ converges to normal distribution, basically a version of central limit. I can't seem to figure out how he did the following calculation:

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Answer 1

$X_j=1$ with probability $1/2$ and $X_j=-1$ with probability $1/2$. So $E[e^{\frac{u}{\sqrt{n}}X_j}] = \frac{1}{2}e^{\frac{u}{\sqrt{n}}1}+ \frac{1}{2}e^{\frac{u}{\sqrt{n}}(-1)}.$