Question 147
Does there exist a sequence $a_1, a_2, \ldots, a_n, \ldots$ of positive real numbers satisfying both of the following conditions:
$\sum_{i=1}^{n} a_i \le n^2$, for every positive integer $n$;
$\sum_{i=1}^{n} \frac{1}{a_i} \le 2008$, for every positive integer $n$?
$\sum_{i=1}^{n} a_i \le n^2$, for every positive integer $n$;
$\sum_{i=1}^{n} \frac{1}{a_i} \le 2008$, for every positive integer $n$?