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

.

Hence

i.e.

.

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!