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!