summation

The value of $\sum_{r=0}^{n} \binom{n}{r}$ is ______.

The value of $$\sum\limits_{n = 0}^\infty {n{{\left( {{1 \over 2}} \right)}^n}\,\,} $$ is _______.

The sum of n terms of the series 4 + 44 + 444 +.... is