Prove that $$ {n \choose 0} - { n \choose 1} + {n \choose 2} - {n \choose 3} + \cdots + (-1)^n{n \choose n} = 0 $$ Note that this equation can also be written as follows: $$ \sum_{i=0}^n {n \choose i}(-1^{i}) = 0 $$ HINT: This can be viewed as a special case of the binomial theorem.