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enter image description here I am revising for an exam that is later today. I'm attempting all questions on past papers. Proof is a topic i've had difficulty with, if someone could check over my answer and give me some improvements for full marks, that'd be fantastic.

enter image description here

Sorry if the image isn't too clear.

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user120993
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1 Answers1

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Your proof is correct. In fact, you just need to rewrite the last formula into to following form to complete the induction:

$take(k+1)=100-2(k+1)$.

Xucheng Zhang
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  • Thanks. I don't follow here the (k+1) one comes from though, whereas I have 2*k? – user120993 Jan 13 '14 at 10:37
  • anyone answer that question please? – user120993 Jan 13 '14 at 10:57
  • @user120993: What you want to show is that the equation $take(n)=100-2n$ holds for $k+1$. This means to replace every instance of $n$ with $k+1$. That is, you want to show that $take(k+1)=100-2(k+1)$. What you have is that $take(k+1)=100-2k-2$. I'm sure you can see why these are the same. For a nice explanation on how induction works check this link: http://math.stackexchange.com/questions/19485/dominoes-and-induction-or-how-does-induction-work/19488#19488 – Apostolos Jan 13 '14 at 11:30