Question 35
The numbers $n(n+1)$, for $n=1,2,3,\ldots,2020$, are written on a board. A child chooses three numbers $a,b,c$ on the board, erases them, and writes the number $\frac{abc}{ab+ac+bc}$ on the board. After $1009$ such operations, one of the remaining numbers is $47$.
- **(a)** Calculate the sum of the reciprocals of the numbers initially written on the board.
- **(b)** Find the other numbers remaining on the board.
- **(a)** Calculate the sum of the reciprocals of the numbers initially written on the board.
- **(b)** Find the other numbers remaining on the board.