Question 15
An open-ended table has two rows. Initially $1,2,\ldots,2005$ occupy the first $2005$ squares of the first row. Each move adds the first two numbers, appends their sum to the end of that row, and drops the two used numbers into corresponding squares in the second row. Continue until one number remains in the first row, then drop it too. Determine the sum of all numbers in the second row. For example, starting with $1,2,3,4,5$ gives $1,2,3,4,5,3,7,8,15$ in the second row, whose sum is $48$.