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Math Help - Need help with induction

  1. #1
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    Need help with induction

    Greetings, I've been trying to solve this question for quite some time now but I just can't figure it out.



    I proved that it works for n=1, now what I need to do is:

    Assuming that:
    is true for every natural number, I need to prove it for n+1, like this:



    So I need to prove that what's on the left is equal to the right. Using the assumption I get this:



    So now I need to take whats on the left and make it look like what's on the right, does anyone know how to do it?

    Thanks in advance.
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  2. #2
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    Re: Need help with induction

    Quote Originally Posted by borab View Post


    So now I need to take whats on the left and make it look like what's on the right, does anyone know how to do it?

    \frac{n(n+1)(2n+1)}{6}+(n+1)^{2}=(n+1)\left[\frac{n(2n+1)+6(n+1)}{6}\right]
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  3. #3
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    Re: Need help with induction

    Hey, thanks for the answer, but I didn't really understand what you did there, can you please explain? Also you still didn't reach

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  4. #4
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    Re: Need help with induction

    Simply put, you just need to factorize one expression in order to get the next one. Plato suggests that you start by putting the (n+1) factor in front. This is given. Then you can work with a simple quadratic expression.
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  5. #5
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    Re: Need help with induction

    Quote Originally Posted by borab View Post
    Hey, thanks for the answer, but I didn't really understand what you did there, can you please explain?
    Also you still didn't reach


    NO I did not.

    That happens to be your job, not mine.

    Hint: Multiply n(2n+1)+6(n+1), combine and factor.
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  6. #6
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    Re: Need help with induction

    I appreciate the help, but I'm afraid I still don't understand what you're telling me to do, it might be because english isn't my first language. Is there any chance you can show the next step?
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Need help with induction

    It appears to me that Plato has left you the task of showing:

    n(2n+1)+6(n+1)=(n+2)(2n+3)
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