Question 130
View rows of $a_{1}, a_{2}, a_{3}, \ldots$ of positive integers. Determine the smallest possible value of $a_{2010}$ if given is: (i) $a_{n}\lt a_{n+1}$ for all $n \geq 1$, (II) $a_{i}+a_{l}\gt a_{j}+a_{k}$ for all foursomes $(i, j, k, l)$ with $1 \leq i\lt j \leq k\lt l$.