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Math Help - Powers

  1. #1
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    Powers

    I have (1+2+...+n)^2 + (n+1)^3

    How do I go about transforming it into (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 (1+2+...+n)^2 + (n+1)^3
    How do I go about transforming it into (1+2+...+n+(n+1))^2?
    Hints:
    (1 + 2 +  \cdots  + n)^2  + (n + 1)^3  = \left[ {\frac{{n(n + 1)}}{2}} \right]^2  + (n + 1)^3
    &
    (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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