How do i complete the proof that that binomial dist is approx normal as n goes to infinity using the moment generating function?

Lim [(1 - p + pe^t)^n] as n goes to infinity.
By Central Limit Theorem it is equal to [e^(npt + ((t^2)/2)np(1-p)]

= Lim n Log [1 - p(1+e^t)]... i am stuck right here.

how do i proceed from here?

Any help is much appreciated.

Thank you