I'm trying to prove the inequality below:
$$ \frac{\sum^{n/2 + \sqrt{n}}_{j=0} {n \choose j}}{2^n} \geq 0.95 $$
I have no idea where to start. I have tried to fill in the formula for small values of n and I see that it holds but I'm unable to proof this. Can anyone give a hint on how to prove this?
Any help would be greatly appreciated.