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