Question

f(x)=x(x+1)(x+2)/3, then f(n)-f(n-1) is equal to?

Answer 1

just plug and chug:

f(n)-f(n-1)
= [n(n+1)(n+2)/3]-[(n+1)((n+1)+1)((n+1)+2)/3]
= -(n+1)(n+2)