Question 69
The numbers $1, 2, \dots, 50$ are written on the blackboard. Ann makes the following operations: she erases any two numbers $a$ and $b$ from the blackboard, writes down to the blackboard one number — the sum $a+b$, afterwards she writes the number $ab(a+b)$ to her notebook. After 49 such operations when only one number left on the blackboard, Ann found the sum $S$ of all 49 numbers which she wrote to her notebook.
a) Prove that $S$ doesn't depend on the order of Ann's operations.
b) Find $S$.
a) Prove that $S$ doesn't depend on the order of Ann's operations.
b) Find $S$.