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!