The integers 1, 2, … , 40 are written on a blackboard. The following operation is then repeated 39
times: In each repetition, 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 at the end?	Choose the correct choice from the following answers
A) 23  B) 122  C) 781  D) 377  E) 272
Initial sum of the number 1 to 40 = n(n+1)2=40×412=840n(n+1)2=40×412=840   After erasing two numbers a and b, and replacing with (a + b − 1), the new sum of the terms of the   sequence = 820 − 1   Similarly, after every operation, the sum of the terms of the sequence reduces by 1.   ∴ The last number left (i.e. final sum) = 820 − 39 = 781   Answer:781
<result>C</result>
The integers 1, 2, … , 40 are written on a blackboard. The following operation is then repeated 39
times: In each repetition, 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 at the end?