If the sum of 4040 consecutive integer numbers is 2020, find out the absolute difference between the first number and the last number.

Let be the smallest of the consecutive integers summing to 2020. Then the largest integer in the sum is so our answer is

For completeness, though, let's solve for the value of that satisfies the conditions of the problem. Recall that the sum of an arithmetic series with first term last term and terms, is Plugging in our known values gives us the equation which simplifies to Thus, so the 4040 consecutive integers are Notice how everything except the cancels out!

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i ran through it by the other answer is wrong