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Question 1122735: The sum of any n consecutive integers is always equal to 100 less than the sum of the next n consecutive integers. Find n
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If it is 100 less, than there will be 100 integers, each 1 less than the corresponding one in the smaller group. The other way to look at it is by comparing lists of both, the second group's having 2 over 100 and 98 under 100, and the largest is exactly 100 more than the smallest.
sum of integers from 1 to 100 is (1/2)(n*(n+1))=5050, when n=100
sum of integers from 1 to 101 is 5151 or (1/2)(101*102). Therefore, sum of the integers from 2 to 101 is 5150
n=100.
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