average of continus series by +1

average of 1 + 2 + 3 + 4 + 5 + 6 + 7 = (1 + 7 ) / 2
average of 1 + 2 + 3 + 4 ... + n = (1 + n ) / 2
ex. average of first 100 number = sum of first 100 number / total number(100 here ) = 5050 / 100 = 50.5 is same as (1 + 100 ) / 2 = 50.5