Carcass wrote:

If x is equal to the sum of the even integers from m to n, inclusive, where m and n are positive even integers, which of the following represents the value of x in terms of m and n?

A. \((\frac{m+n}{2})(\frac{n-m}{2} + 1)\)

B. \(3(m+n)\)

C. \(\frac{n^2 - m^2}{2}\)

D. \(6(m+n)\)

E. \((\frac{m+n}{2})(\frac{n-m}{2})\)

This is how I did...

since x is sum of m to n inclusive where m and n are even.

Let take such series => case 1: 2, 4 and 6 (or ) case 2: 2, 4, 6 and 8

Sub since m is starting and n is ending of the series.

case 1: x sum is = 12

m = 2 and n = 6 , sub in the options we get A as 12.

case 2: x sum is 20

m = 2 and n = 8 , sub in the options we get A as 20

Hence A.