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Thread: Powers

  1. #1
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    Powers

    I have $\displaystyle (1+2+...+n)^2 + (n+1)^3 $

    How do I go about transforming it into $\displaystyle (1+2+...+n+(n+1))^2$?
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  2. #2
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    Re: Powers

    Quote Originally Posted by spruancejr View Post
    I have $\displaystyle (1+2+...+n)^2 + (n+1)^3 $
    How do I go about transforming it into $\displaystyle (1+2+...+n+(n+1))^2$?
    Hints:
    $\displaystyle (1 + 2 + \cdots + n)^2 + (n + 1)^3 = \left[ {\frac{{n(n + 1)}}{2}} \right]^2 + (n + 1)^3 $
    &
    $\displaystyle (1 + 2 + \cdots + n+(n+1))^2 = \left[ {\frac{{(n+1)(n + 2)}}{2}} \right]^2 $
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  3. #3
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    Re: Powers

    Thanks! It's so simple and beautiful now...
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