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.
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.
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.
Hope that was clear enough.
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
Once again, hope that made sense...