1. ## Proving an inequality

I'm trying to prove that for and I don't think I have done it correctly.

As far as I know I need to re-arrange the inequality into an equivalent form and then put n=3 in to see if it is true.

Here is what I did.

then divide by 7 to give

the minus the power of two away from each side to give

which is

So the inequality is true for ???????????

2. ## Re: Proving an inequality

Originally Posted by jezb5
I'm trying to prove that for and I don't think I have done it correctly.

I think that you have completely missed the point.
This should be done using induction with base case of $\displaystyle n=3$.

Then assume it is true for $\displaystyle K>3$ and show that implies it is true for $\displaystyle K+1$.

3. ## Re: Proving an inequality

Originally Posted by Plato
I think that you have completely missed the point.
This should be done using induction with base case of $\displaystyle n=3$.

Then assume it is true for $\displaystyle K>3$ and show that implies it is true for $\displaystyle K+1$.
I think I'm a bit lost as my book only explains that I re-arrange the inequality into an equivalent form and this final inequality is true.

As an example it says prove that

for

it then says by rearranging this inequality into an equivalent form we get

and then this final inequality is true for

4. ## Re: Proving an inequality

Originally Posted by jezb5
I think I'm a bit lost as my book only explains that I re-arrange the inequality into an equivalent form and this final inequality is true.
As an example it says prove that
for
it then says by rearranging this inequality into an equivalent form we get

and then this final inequality is true for
Not being the author of your text, I have no idea what any of that means.
As I said before, this question is tailor maid for proof by induction.

Have you studied induction?