Question 3
The $2010$ positive real numbers $a_1,a_2,\ldots,a_{2010}$
satisfy the inequality $a_i a_j \le i+j$
for all $1 \le i \lt j \le 2010$.
Determine, with proof, the largest possible value
of the product $a_1a_2\ldots a_{2010}$.
Proposed by Gabriel Carroll (credit in the supplied third-party notes).
satisfy the inequality $a_i a_j \le i+j$
for all $1 \le i \lt j \le 2010$.
Determine, with proof, the largest possible value
of the product $a_1a_2\ldots a_{2010}$.
Proposed by Gabriel Carroll (credit in the supplied third-party notes).