I have no idea how to do this......

Any help will be apreaciated

Let $\displaystyle \{ Xn\} _{n \ge 1}^{}$ be a sequence of iid random variabled such that $\displaystyle E({X_1}) = \mu $ and $\displaystyle V({X_1}) = {\sigma ^{^2}}$.

Consider the sequence of real numbers: $\displaystyle {\{ {a_n}\} _{n \ge 1}}$

Proof that:

$\displaystyle P(\frac{{{S_n} - E({S_n})}}{{V({S_n})}} \le {a_n}) - \Phi ({a_n}) \to 0$

Where:

$\displaystyle {S_n} = \sum\limits_{i = 1}^n {{X_i}} $

Edit: I know I have to use Central limit theorem, but I'm doubtful cuz of that a_n thing inside PHI