zmudz
  • zmudz
Let \(a_1, \ldots, a_n\) be distinct positive integers. Show that \(\frac{a_1}{1^2} + \frac{a_2}{2^2} + \cdots + \frac{a_n}{n^2} \geq \frac{1}{1} + \frac{1}{2} + \cdots + \frac{1}{n}.\)
Mathematics
jamiebookeater
  • jamiebookeater
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tkhunny
  • tkhunny
What is the least value of the LHS?
zmudz
  • zmudz
@tkhunny I'm not sure. How do you figure out?
tkhunny
  • tkhunny
Distinct, positive integers. What is the least of those? Second least? Third...?

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