# Math Help - how do you prove this using induction

1. ## how do you prove this using induction

can you help me with this question

2. ## Re: how do you prove this using induction

That looks pretty straight forward to me. Obviously when n= 0 or 1, $f(0)= 0< 1= 5^0$ and $f(1)= 1< 5= 5^1$.

Now, suppose that $f(k)< 5^k$ for all k< n. Then $f(n+1)= 3f(n)+ 10f(n-1)< 3(5^n)+ 10(5^{n-1})$.

Can you simplify that?

3. ## Re: how do you prove this using induction

does it become f(n+1)=3f(n)+10f(n-1)<5^(n+1)

4. ## Re: how do you prove this using induction

It's basic arithmetic: factor $5^{n}$ out of $3(5^n)+ 10(5^{n-1})$. What is left?