# Thread: Strong Induction Problem using Summations

1. ## Strong Induction Problem using Summations

Let an be the recurrence defined by $a_{0} = 1$ (for all n > 0)
$a_{n} = 1 + \sum_{i=0}^{n-1}a_{i}$

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

Any help is appreciated!

2. Originally Posted by tshare1
Let an be the recurrence defined by a0 = 1 (for all n > 0)
$a_{n} = 1 + \sum_{i=0}^{n-1}$

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

Any help is appreciated!
I think you have a typo

3. Sorry, I was figuring out the latex thing.