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 sum of the numbers left on the board at the end?	Choose the correct option:  A) 820  B) 821  C) 781  D) 819  E) 780
Explanation :   Initial sum of the numbers is 1 + 2 + …40.   Initial sum = 40 * 41/2= 
<gadget id="calculator">40 * 41/2</gadget>
<output>820</output>
820. (A.P. with common difference 1 and 1st term 1, last term 40).   Two numbers, a, b are erased and replaced by a+b-1, that means, the sum is now 819.   This is done 39 times. So, sum after 39 time replacement is 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 sum of the numbers left on the board at the end?