You can put this solution on YOUR website! The Sum of first n consecutive integers = n* (n+1)/2
Sum of the first 300 integers = 300 * 301/2
Sum of first 250 integers = 250 * 251/2
Hence Sum of integers between 250 and 300 is
= 300*301/2 - 250*251/2
= 150*301 - 125*251
= 25* (6*301 - 5*251)
= 25 * (1806 - 1255)
= 25 * 551
= 13775
Hence Sum of integers between 250 and 300 is 13775