Strong Induction for Fibonacci I'm a little lost of how to use strong induction to prove the following for the Fibonacci sequence: 
$F_n < 2^n$ for all natural numbers 
Any help would be very much appreciated!!

Note that $F_1=1<2^1$ and $F_2=1<2^2$, so $F_n<2^n$ is true for $n=1$ and $n=2$.
Now, suppose that $F_n<2^n$ for some $n$. 
Then $F_{n+1} = F_n+F_{n-1}\le 2\cdot F_n < 2\cdot 2^n = 2^{n+1}$.
So, by induction, $F_n<2^n$ for all $n\in\mathbb{N}$.
