I was hoping someone could help me with a proof. I have attached an image.

I am going to prove it using induction (rather than well-ordering), and the base cases where n=1,2 and 3 are straightforward.

Thank you in advance.

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- February 23rd 2008, 08:34 PMshawnMathematical Induction Question
I was hoping someone could help me with a proof. I have attached an image.

I am going to prove it using induction (rather than well-ordering), and the base cases where n=1,2 and 3 are straightforward.

Thank you in advance. - February 23rd 2008, 10:14 PMJen
Inductive Hypothesis:

Show:

Working with the left side...

On the right hand side we have 5/4 times our inductive hypothesis, substituting we get...

Because k>4

So, by transitivity, we get...

"Which Was What We Wanted"

Sorry I didn't know how to do the greater than or equal to symbol. (Crying)

Hope that was clear enough. - February 23rd 2008, 10:27 PMJhevon
- February 23rd 2008, 10:27 PMJen
Oooops, lets try this again.

- February 23rd 2008, 10:29 PMshawn
Thank you very much Jen. Now I just need to do c using part b as my solution.

- February 23rd 2008, 10:40 PMJen
Given that:

Show:

Using the given inequality... (multiply both sides by , note that this is legal because exponential functions are non-negative)

Adding to both sides we get...

The inequality on the right is possible because x is always greater than or equal to 2 so x/2 is always greater than or equal to 1.

Once again by transitivity we get

(Clapping)

Once again, hope that made sense...