Problem: If f(n)=31​n(n+1)(n+2), then f(r)−f(r−1) equals:
Answer Choices:
A. r(r+1)
B. (r+1)(r+2)
C. 31​r(r+1)
D. 31​(r+1)(r+2)
E. 31​r(r+1)(2r+1)
Solution:
f(r)−f(r−1)=31​r(r+1)(r+2)−31​(r−1)(r)(r+1)=31​r(r+1)(r+2−r+1)
=r(r+1).