Multiple choice general knowledge math & puzzles

The integers 1,2,3,...40 are written on a blackboard.The following operation is then repeated 39 times.In each repeatition any two numbers ,say a and b,currently on the blackboard are erased and a new number a+b-1 is written.What will be the number left on the board then?

  1. 781

  2. 820

  3. 819

  4. 780

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initially, sum = 1+2+...+40 = 40×41/2 = 820. In each operation, we replace a and b with a+b-1, so the sum changes from (a+b) to (a+b-1), decreasing by 1. After 39 such operations, the sum decreases by 39, giving 820 - 39 = 781. This final number is what remains.