Someone check this proof please

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  1. member910132's Avatar
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    Someone check this proof please
    I do a lot of proof by induction questions and would appreciate it if someone could tell me whether I would get all the marks in the exam based on my layout.
    Here is a picture of my answer, in exam conditions, to q6b on here:
    http://store.aqa.org.uk/qual/gce/pdf...W-QP-JUN11.PDF
    MS : http://store.aqa.org.uk/qual/gce/pdf...W-MS-JUN11.PDF

    The pic follows below.

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    Last edited by member910132; 21-05-2012 at 12:07.
  2. member910132's Avatar
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    Here


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  3. ninuzu's Avatar
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    Re: Someone check this proof please
    Looks good to me. Have you done a basis case (where n=1)? I know that you have to do this for OCR.
  4. member910132's Avatar
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    Yea, at the end.

    Can anyone check my answer to q7b on the same paper, my answer differs to theirs slightly but I think I am still correct.


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  5. ninuzu's Avatar
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    Re: Someone check this proof please
    (Original post by member910132)
    Yea, at the end.

    Can anyone check my answer to q7b on the same paper, my answer differs to theirs slightly but I think I am still correct.


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    Oh sorry, didn't see it I think maybe though, and I know it seems stupid, SHOW that n=1 works for both what they give you and what they are asking you to prove.
  6. member910132's Avatar
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    Re: Someone check this proof please
    (Original post by ninuzu)
    Oh sorry, didn't see it I think maybe though, and I know it seems stupid, SHOW that n=1 works for both what they give you and what they are asking you to prove.
    I have, I showed it for  (2n-1)^2 and  \frac13 n(4n^2-1)

    Any light to shed on q7b ?

    Lastly, on this paper the Last question says show that sum of the roots of that equation (refer to the paper and MS) = 5,

    In the MS we get to here :  \tan^2 \frac{\pi}{5} + \tan^2 \frac{2\pi}{5} = 5 and so the next step is obviously  \tan \frac{\pi}{5} + \tan \frac{2\pi}{5} = \sqrt{5} and unless we are solving for for an unknown variable, we always take  \sqrt{5} as it's positive value, but to get 2 out of the 5 marks we had to show it equaled  \pm \sqrt{5} and then give a reason why we reject the negative ???? But I thought it is understood that  \sqrt{5} = +\sqrt{5} and we only use the +/- when we have something like  x^2 = 5 \imples x = \pm \sqrt{5} . Can anyone explain this ?

    Anyway, would it of been sufficient to that both tan pi/5 and tan 2pi/5 are positive and so we reject - sqrt 5 ?

    But there was a massive thread a while back in which the best mathematicians on here said that sqrt 5 = + sqrt 5 unless you are solving for an unknown.
    Last edited by member910132; 21-05-2012 at 11:57.
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    Re: Someone check this proof please
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