Given that the sum of the 1st n positive integers is 5053. Which integer is counted twice.?

Answer 1

The sum of the first one hundred integers (that is, 1 + 2 + 3 + .. + 100) = 5050.

It looks like the 3 is counted twice to get 5053. But is that the only possibility? The sum of the first 99 integers is 4950, and adding even 99 isn't enough to reach 5050, much less 5053. Therefore the first guess is correct; n = 100, and the three is counted twice.

Answer 2

3