Hi! Can anyone please help me with the following proof:
Show that .
I have to show this using the AM/GM inequality, imitating the proof that for and considering .
This is how I proved that for :
The Arithmetic/Geometric mean inequality states that, given non-negative ,
Now I apply the AM/GM inequality to the numbers and .
Then and .
Now, if , then
and hence as by the sandwich theorem.
If , then where . But as and hence
as by the combination theorem.
Any ideas how to prove imitating the above proof and considering ? I'd appreciate any help!