If we have the equality so assume, wlog, that and that
We then have to prove that
Now,
so,
If then and the result follows, so assume that and that with
Then,
,
and again the result follows.
Hello everyone.
I would like to start 'marathon' of the exercises from different competition in the secondary school level. (ages 15-18)
let's start with inequality
Exercise 1.
Let be positive real numbers. Prove that
where is natural.
Enjoy!