Hello,

Could someone help me prooving the following:

If

then

for all natural numbers.

I hope that i have written everything correctly (this is my first time).

NB! How do i type in equations and stuff?

Thank you very much.

Printable View

- February 21st 2010, 08:56 PMsurjectiveproof by induction
Hello,

Could someone help me prooving the following:

If

then

for all natural numbers.

I hope that i have written everything correctly (this is my first time).

NB! How do i type in equations and stuff?

Thank you very much. - February 21st 2010, 09:29 PMo_O
Please no double posting. On typing math symbols, see this thread for more: LaTex Tutorial

You can see the code that generates the image by clicking on it.

As for your problem, let's look at the inductive step.**Assuming**that , our goal is to prove that .

Looking at the LHS, notice that:

Now I highlighted the part in red for a reason .. and it shouldn't be too hard to show that this is bigger than . - February 22nd 2010, 12:30 AMsurjectiveProof by induction
Hello again,

Sorry for the inconvenience. The thing is that what you mentioned before is exactly what I have already done . . . and then I get stuck. I can't seem to get the "great idea" (maybe because I havn't slept all night).

What I'm trying to do is to reach the conslusion (instead of showing the truthfulness of an inequality):

Now from calculus I know that:

Using the inductive step we may write:

This is where I get stuck.

Your help is greatly appreciated.

Thanks. - February 22nd 2010, 03:21 AMArchie Meade
- February 22nd 2010, 04:18 AMsurjectiveProof by induction
Hello,

Thank you very much. It seems that I was only one step away from completing the proof. Thank you all very much.