For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?	Options
A) X(X+1)/2 + Y(Y+1)/2
B) X(X+1)/2 - Y(Y-1)/2
C) X(X+1)/2 - Y(Y+1)/2
D) X(X+1)/2 + Y(Y-1)/2
E) X(Y+1)/2 - Y(X-1)/2
The sum of all the integers between X and Y,inclusiveis the sum of the first X positive integersminusthe sum of the first Y-1 positive integers.   The sum of the first X positive integers is X(X+1)/2;   The sum of the first Y-1 positive integers is (Y-1)Y/2;   Therefore the answer is X(X+1)/2 - (Y-1)Y/2.   Answer: X(X+1)/2 - Y(Y-1)/2.
<result>B</result>
For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?