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Math Help - Proving an inequality

  1. #1
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    Proving an inequality

    I'm trying to prove that Proving an inequality-math_image.gif for Proving an inequality-math_image-2-.gif and I don't think I have done it correctly.

    As far as I know I need to re-arrange the inequality into an equivalent form and then put n=3 in to see if it is true.

    Here is what I did.

    Proving an inequality-math_image-3-.gif

    Proving an inequality-math_image-4-.gif

    then divide by 7 to give

    Proving an inequality-math_image-5-.gif

    the minus the power of two away from each side to give

    Proving an inequality-math_image-6-.gif

    which is

    Proving an inequality-math_image-7-.gif


    So the inequality Click image for larger version. 

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ID:	27379 is true for Click image for larger version. 

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ID:	27381 ???????????
    Attached Thumbnails Attached Thumbnails Proving an inequality-math_image-1-.gif  
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  2. #2
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    Re: Proving an inequality

    Quote Originally Posted by jezb5 View Post
    I'm trying to prove that Click image for larger version. 

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ID:	27379 for Click image for larger version. 

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ID:	27381 and I don't think I have done it correctly.

    I think that you have completely missed the point.
    This should be done using induction with base case of n=3.

    Then assume it is true for K>3 and show that implies it is true for K+1.
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  3. #3
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    Re: Proving an inequality

    Quote Originally Posted by Plato View Post
    I think that you have completely missed the point.
    This should be done using induction with base case of n=3.

    Then assume it is true for K>3 and show that implies it is true for K+1.
    I think I'm a bit lost as my book only explains that I re-arrange the inequality into an equivalent form and this final inequality is true.

    As an example it says prove that

    Proving an inequality-math_image-8-.gif for Proving an inequality-math_image-9-.gif

    it then says by rearranging this inequality into an equivalent form we get

    Proving an inequality-math_image-10-.gif

    and then this final inequality is true for Click image for larger version. 

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ID:	27388
    Last edited by jezb5; March 6th 2013 at 07:09 AM.
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  4. #4
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    Re: Proving an inequality

    Quote Originally Posted by jezb5 View Post
    I think I'm a bit lost as my book only explains that I re-arrange the inequality into an equivalent form and this final inequality is true.
    As an example it says prove that
    Click image for larger version. 

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ID:	27387 for Click image for larger version. 

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ID:	27388
    it then says by rearranging this inequality into an equivalent form we get
    Click image for larger version. 

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ID:	27389
    and then this final inequality is true for Click image for larger version. 

Name:	math_image (9).gif 
Views:	4 
Size:	1.4 KB 
ID:	27388
    Not being the author of your text, I have no idea what any of that means.
    As I said before, this question is tailor maid for proof by induction.

    Have you studied induction?
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