Hello.
Now only the first step:
Skrytý text:Let

and

. Then

.
The second step.
Skrytý text:Obviously
1.

2. for each

holds:

i. e.
for each

holds:

.
Hence the succession

is increasing.
The third step.
Skrytý text:For each

:

,

,

,
i. e.

because of

.
Hence

for

because of

for

.
Finnishing :
Skrytý text: When

is positive and increasing, then

, where

, is decreasing.
Hence

.