This question popped up in my revision sheet, and was just wondering on how to do it (this is high-school math by the way, so nothing too complicated please)
"Expand $(x+(1-x))^n$, and use this to prove: $nC0+nC1+nC2+...+nCn=2^n$"
I literally have no idea on how to do this, any help would be appreciated.
We have
$$1=(x+(1-x))^n=\sum_{k=0}^n{n\choose k}x^k(1-x)^{n-k}$$ Now let $x=\frac12$. Can you take it frome here?