IMO Shortlist 1978 problem 6
Dodao/la:
arhiva2. travnja 2012. Let
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
be an injective function from
![{1,2,3,\ldots}](/media/m/c/c/e/cce0427677c86c3baccfccf81bd9efcd.png)
in itself. Prove that for any
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
we have:
%V0
Let $f$ be an injective function from ${1,2,3,\ldots}$ in itself. Prove that for any $n$ we have: $\sum_{k=1}^{n} f(k)k^{-2} \geq \sum_{k=1}^{n} k^{-1}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1978