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Math Help - University Algebra Problem

  1. #1
    Junior Member
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    University Algebra Problem

    I know the first step (plugging in a number like 2) and seeing if it works, but I have trouble when it comes to inserting "k" and "k+1".

    Prove by induction that
    1^3+....n^3=(1+.....n)^2.

    Any help appreciated.

    Mike
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  2. #2
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    You have to show that,
    1^3+2^3+3^3+...+n^3=n^2(n+1)^2/4

    Then, show that,
    1+2+...+n=n(n+1)/2

    Thus, since we see that if we square the bottom one then we get the top one, proof complete.

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