<p>If <img alt="$f(n)=\tfrac{1}{3} n(n+1)(n+2)$" height="21" src="https://latex.artofproblemsolving.com/7/c/d/7cd8367e6fd8a2ed43cc1b2105a2ba30125b3c08.png" width="192" />, then <img alt="$f(r)-f(r-1)$" height="18" src="https://latex.artofproblemsolving.com/1/c/3/1c3c5694bc547b9e68eb38ca8eaae74269c2d398.png" width="119" /> equals:</p> <p><img alt="$\text{(A) } r(r+1)\quad \text{(B) } (r+1)(r+2)\quad \text{(C) } \tfrac{1}{3} r(r+1)\quad \\ \text{(D) } \tfrac{1}{3} (r+1)(r+2)\quad \text{(E )} \tfrac{1}{3} r(r+1)(2r+1)$" height="43" src="https://latex.artofproblemsolving.com/c/1/b/c1b51ee7deee086abefcbf0d6612cb9edf4a2092.png" width="368" /></p>

Question No: 480

If $f(n)=\tfrac{1}{3} n(n+1)(n+2)$ , then $f(r)-f(r-1)$ equals:

$\text{(A) } r(r+1)\quad \text{(B) } (r+1)(r+2)\quad \text{(C) } \tfrac{1}{3} r(r+1)\quad \\ \text{(D) } \tfrac{1}{3} (r+1)(r+2)\quad \text{(E )} \tfrac{1}{3} r(r+1)(2r+1)$

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Tags: Algebra

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