BALKAN 2008 Problem 2

Does there exist a sequence $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ of positive real numbers satisfying both of the following conditions: (i) $\sum_{i=1}^{n} a_{i} \leq n^{2}$, for every positive integer $n$; (ii) $\sum_{i=1}^{n} \frac{1}{a_{i}} \leq 2008$, for every positive integer $n$ ?