# Proving an inequality

• March 6th 2013, 06:36 AM
jezb5
Proving an inequality
I'm trying to prove that Attachment 27379 for Attachment 27381 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.

Attachment 27382

Attachment 27383

then divide by 7 to give

Attachment 27384

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

Attachment 27385

which is

Attachment 27386

So the inequality Attachment 27379 is true for Attachment 27381 ???????????
• March 6th 2013, 06:41 AM
Plato
Re: Proving an inequality
Quote:

Originally Posted by jezb5
I'm trying to prove that Attachment 27379 for Attachment 27381 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 $n=3$.

Then assume it is true for $K>3$ and show that implies it is true for $K+1$.
• March 6th 2013, 07:05 AM
jezb5
Re: Proving an inequality
Quote:

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

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

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

Attachment 27387 for Attachment 27388

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

Attachment 27389

and then this final inequality is true for Attachment 27388
• March 6th 2013, 07:17 AM
Plato
Re: Proving an inequality
Quote:

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
Attachment 27387 for Attachment 27388
it then says by rearranging this inequality into an equivalent form we get
Attachment 27389
and then this final inequality is true for Attachment 27388

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?