Statement of the classical CLT

What does the Central Limit Theorem say?

Standardised sums of i.i.d. variables with finite variance converge in distribution to a standard normal. If $X_1,X_2,\dots$ are i.i.d. with mean $\mu$ and variance $\sigma^2<\infty$, then $\dfrac{X_1+\dots+X_n-n\mu}{\sigma\sqrt n}\to N(0,1)$ as $n\to\infty$, whatever the shape of the original distribution.