Hi I need help with these questions on binomial theorem!

1.) From the binomial expansion of $\displaystyle (1+x)^n$, deduce that

$\displaystyle {2n+1 \choose 0}+{2n+1 \choose 1}+{2n+1 \choose 2}+...+{2n+1 \choose n}=4^n$

Using T( r+1) I know the coefficient of $\displaystyle x^n$ is $\displaystyle {2n+1 \choose n}$. I had let n in $\displaystyle {n \choose r}$ be 2n+1 and x be 1.

That way, I got $\displaystyle (2)^{2n+1}$ Is this wrong because from here, I do not know how to get $\displaystyle 4^n$

2.) By considering the binomial expansion of $\displaystyle (1+x)^n$, find $\displaystyle \sum\limits_{r=0}^n2^r{n \choose r}$

I got $\displaystyle 2^n$ as an answer for this one, I had just expanded out the summation and then let x=1. It's wrong..

Thank you so much!