Summations and Combinations

Prove the following : 1. $$\sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k {n-k \choose k} \cdot 2^{n-2k} = n + 1$$ 2. $$\sum_{k=0}^n {2k \choose k}{2n-2k \choose n-k} = 4^n$$ 3. $$\sum_{k=0}^{n} 2^k {n \choose k}{n-k \choose \lfloor(n-k)/2\rfloor} = {2n+1 \choose n}$$