3
$\begingroup$

Let $a_1$, $a_2$,..., $a_n$ be the sequence of positive numbers, and let $b_1$, $b_2$,..., $b_n$ be any permutation of the first sequence. Show that $$\frac{a_1}{b_1}+\frac{a_2}{b_2}+...+\frac{a_n}{b_n} \geq n$$

This is a preparation Question PUTNAM contest. The theme of the section is "inequality". I can not make the problem from inequality. Is anyone is able give me a hint (using inequalities)?

$\endgroup$
7
$\begingroup$

Hint: AM-GM. Note that the product of our fractions is $1$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy