Proof by Induction
Maths and statistics discussion, revision, exam and homework help.
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Re: Proof by InductionI hadn't noticed you'd suggested that. The reason I wasn't keen to suggest expanding everything is that (as in raheem94's post) you get a lot of terms, and I'm not convinced that manipulating those would be easier than keeping it 'as factorized as possible' whilst doing the working.(Original post by Mr M)
I suggested expanding it all for a reason, students with less ability than you struggle with anything but the simplest factorisation.
I could perhaps have been clearer about the +1 not being included in the common factor, though. (But I did mention it in a previous post.) -
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Re: Proof by InductionYou only get 5 terms?!(Original post by nuodai)
I hadn't noticed you'd suggested that. The reason I wasn't keen to suggest expanding everything is that (as in raheem94's post) you get a lot of terms, and I'm not convinced that manipulating those would be easier than keeping it 'as factorized as possible' whilst doing the working.Last edited by Mr M; 07-05-2012 at 17:11. -
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Re: Proof by InductionI like to look at the final answer i should get, and try to expand it, to see which steps i need to do to get the answer.(Original post by nuodai)
I hadn't noticed you'd suggested that. The reason I wasn't keen to suggest expanding everything is that (as in raheem94's post) you get a lot of terms, and I'm not convinced that manipulating those would be easier than keeping it 'as factorized as possible' whilst doing the working.
I could perhaps have been clearer about the +1 not being included in the common factor, though. (But I did mention it in a previous post.) -
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Re: Proof by InductionI think this must be a matter of style that varies from person to person. I find it much easier to make mistakes when I have a collection of terms that look similar (owing, for example, to having common factors) than I do by keeping the common factors out of the manipulation as much as possible. I suppose others might find it hard to look at an expression with lots of brackets and separate in their minds what stays the same and what doesn't.(Original post by Mr M)
You only get 5 terms?!
Like I say, matter of style.Last edited by nuodai; 07-05-2012 at 17:18. -
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Re: Proof by InductionCommon factors is by far the best method. Weaker students are unable to do it though but they often can experience success by expanding, collecting like terms and then factorising.(Original post by nuodai)
I think this must be a matter of style that varies from person to person. I find it much easier to make mistakes when I have a collection of terms that look similar (owing, for example, to having common factors) than I do by keeping the common factors out of the manipulation as much as possible. I suppose others might find it hard to look at an expression with lots of brackets and separate in their minds what stays the same and what doesn't. -
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Re: Proof by InductionI think I'll have to bow to your superior experience on this one. I suppose it can't hurt for the OP to see two equivalent methods.(Original post by Mr M)
Common factors is by far the best method. Weaker students are unable to do it though but they often can experience success by expanding, collecting like terms and then factorising.
