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Math Help - Proof question

  1. #1
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    Proof question

    I have a question that's giving me a hard time and im not sure how to go about solving it...

    Prove that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 while n>= 1

    im a little lost at what to do after testing it out for n = 1 and proving that true.
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  2. #2
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    Quote Originally Posted by JoeBabble View Post
    I have a question that's giving me a hard time and im not sure how to go about solving it...

    Prove that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 while n>= 1

    im a little lost at what to do after testing it out for n = 1 and proving that true.
    Mathematcal Induction

    For P(1):

    Put n=1
    RHS =LHS
    Hence our assumption is correct for n=1

    Assumption P(K):

    Let the above statement be correct for n=k
    Hence

    1^3 + 2^3 + ... + k^3 = [k(k+1)/2]^2.............................1

    Prove it For P(k+1):

    So LHS will be



    1^3 + 2^3 + ... + k^3 + (k+1)^3

    Now for terms till n=k put the values obtained in (1)


    [k(k+1)/2]^2 + (k+1)^3

    On simplifying the above thing you will get

    [(k+1)(k+2)/2]^2

    This proves that the statement is correct for n = (k+1) when its correct for n= k

    Hence through the principle of mathematical induction we have proved that the statement is correct
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