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Math Help - Prove the following by induction

  1. #1
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    Prove the following by induction

    I am completely aware of what I need to be doing to prove something by induction, except my algebra skills are too crappy to do it.

    For example

    prove the following by induction...

    1^3 + 2^3 + 3^3 + ... + n3 = n^2(n+1)^2/4

    I have already proved this is the case for n=1 and n=2

    Then I say suppose it holds for n=k where k>=1

    k^2(k+1)^2/4

    Then I have to show it holds for k+1

    So I have to show that....

    (k+1)^2[(k+1)+1]^2/4 = k^2(k+1)^2/4 + (k+1)^2

    Is this correct?

    If it is how do i even start here. I noticed that they both have a (k+1)^2 term so i started by pulling that out front. I just get so lost from there...
    Last edited by ehpoc; November 17th 2011 at 02:08 PM.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Prove the following by induction

    You start by correctly stating the problem!
    How on earth are you supposed to see that "13" is NOT thirteen, but rather "1^3"?!?!

    You can prove that the sum of the first n cubes is the square of the sum of the first n squares, btw...
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  3. #3
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    Re: Prove the following by induction

    sorry I never noticed when I copy and pasted

    You can prove that the sum of the first n cubes is the square of the sum of the first n squares, btw...
    no clue what you are saying LOL
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  4. #4
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    Re: Prove the following by induction

    he is saying:

    \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k^2\right)^2

    although this is incorrect, the actual formula is:

    \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2
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  5. #5
    Super Member TheChaz's Avatar
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    Re: Prove the following by induction

    Quote Originally Posted by Deveno View Post
    he is saying:

    \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k^2\right)^2

    although this is incorrect, the actual formula is:

    \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2
    The latter is what I wanted to say! I lose track of my prepositional phrases sometimes
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