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