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Math Help - [SOLVED] math induction

  1. #1
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    [SOLVED] math induction

    can someone help me with this problem? i have to prove that the summation of i^3=(n(n+1)/2)^2
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    Quote Originally Posted by needhelp101 View Post
    can someone help me with this problem? i have to prove that the summation of i^3=(n(n+1)/2)^2
    TO prove with mathematical induction follow these steps

    1) Proof for n = 1
    Just prove that it is true if we keep the value of n = 1

    2)Assume for n= k

    Assume that the given statement is correct for n=k
    .................................
    in your question
    Assume
    1^3 +2^3 +.....k^3 = (k(k+1)/2)^2


    3) Using step 2(the assumption we made) to Prove the statement for n = k+1

    ...............

    in your case prove that

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

    using
    1^3 +2^3 +.....k^3 = (k(k+1)/2)^2-------------(1)

    So put (1) in the LHS thus

    =(k(k+1)/2)^2 + (k+1)^3


    Now simplify this LHS to get (\frac{(k+1)(k+2)}{2})^2
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    it was that last part where i'm stuck at. i'm not sure if the [(k+1)(k+2)/2]^2 is the answer.
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  5. #5
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    Quote Originally Posted by needhelp101 View Post
    it was that last part where i'm stuck at. i'm not sure if the [(k+1)(k+2)/2]^2 is the answer.
    Do you understand proof by induction? If so, you will appreciate that this result is what step 3 required.

    Since this question has been asked and solved in another thread, this thread is closed.
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