Question

Let \(a_1, \ldots, a_n\) be distinct positive integers. Show that

\(\frac{a_1}{1^2} + \frac{a_2}{2^2} + \cdots + \frac{a_n}{n^2} \geq \frac{1}{1} + \frac{1}{2} + \cdots + \frac{1}{n}.\)

Answer 1

What is the least value of the LHS?

Answer 2

@tkhunny I'm not sure. How do you figure out?

Answer 3

Distinct, positive integers. What is the least of those? Second least? Third...?