SOLUTION: if f(n)=1/3n(n+1)(n+2), then find f(r)-f(r-1) in simplest form.

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Question 1178378: if f(n)=1/3n(n+1)(n+2), then find f(r)-f(r-1) in simplest form.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

For a minute, forget about the factor of  (1/3)  and work with the numerators only


    r*(r+1)*(r+2) - (r-1)*r*(r+1) = r*(r+1) * [ (r+2) - (r-1) ] = 3r*(r+1).



Now recall about this factor (1/3) and get


    f(r) - f(r-1) = r*(r+1)


in the simplest form.

Solved.