Let an be the recurrence defined by $\displaystyle a_{0} = 1$ (for all n > 0)

$\displaystyle a_{n} = 1 + \sum_{i=0}^{n-1}a_{i}$

Prove using strong induction that (for all n greater than or equal to 0) $\displaystyle a_{n} = 2^{n}$

Any help is appreciated!