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Math Help - Induction Emergency!

  1. #1
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    Unhappy Induction Emergency!

    I have a test tomorrow and I'm really confused on induction. I was able to figure out one of my homework problems, but I'm having trouble with this one:

    Directions - Use mathematical induction to prove the given formula for every positive integer n.


    I could really use help! Thanks!
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  2. #2
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    \sum_{i=1}^{n+1} i(i+1) =

    \left[ \sum_{i=1}^n i(i+1) \right] + (n+1)(n+2) =

    \frac{n(n+1)(n+2)}{3} + (n+1)(n+2) =

    \frac{n(n+1)(n+2)}{3} + \frac{3(n+1)(n+2)}{3} =

    \frac{n(n+1)(n+2) + 3(n+1)(n+2)}{3} =

    \frac{(n+1)(n+2)(n + 3)}{3} = \sum_{i=1}^{n+1} i(i+1)
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