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Math Help - Inductive Proof

  1. #1
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    Inductive Proof

    how do you get this problem [k(k+1)/2]^2 + (k+1)^3 down to [(k+1)(k+2)/2]^2

    I'm having troubles with the arithmetic...
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  2. #2
    Senior Member roninpro's Avatar
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    Wait, is this true?

    Factor (k+2)^2 out to get (k+1)^2\left(\frac{k}{2}+(k+1)\right). Then combine the terms by getting a common denominator. But, it doesn't seem to give you what claim it does.
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  3. #3
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    Yeah I don't get this one either =/
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  4. #4
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    so i factored out (k+1)^2 and i got this....1/4(k+1)^2 + (K^2+(k+1))
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  5. #5
    Senior Member roninpro's Avatar
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    Ah, oops. I factored it incorrectly, myself.

    You should have <br />
(k+1)^2\left(\frac{k^2}{4}+(k+1)\right)=(k+1)^2\le  ft(\frac{k^2+4k+4}{4}\right)=(k+1)^2\frac{(k+2)^2}  {4}<br />

    This gives it to you.
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  6. #6
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    thanks man!
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