Question 130
Suppose that the combination $(n; a_1, a_2, \dots, a_n)$ of positive integers satisfy the condition $a_1 + a_2 + \dots + a_n = 2008$. Let for each $k$ with $1 \le k \le n$, $A_k = a_1a_2\cdots a_k$. Determine the maximum possible value that the quantity $A_1 + A_2 + \dots + A_n$ can take.