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Thread: Greatest Term

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    Greatest Term

    When doing questions in binomial to find the greatest term, we first have to take a ratio of T(r+1)/T(r). But my question is that do we have to derive the ratio every time or can we just directly write T(r+1)/T(r)= (n-r+1)/r * b/a?
    Last edited by Green Yoda; 22 Aug 2017 at 12:04 PM.
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    Re: Greatest Term

    Quote Originally Posted by Green Yoda View Post
    When doing questions in binomial to find the greatest term, we first have to take a ratio of T(r+1)/T(r). But my question is that do we have to derive the ratio every time or can we just directly write T(r+1)/T(r)= (n-r+1)/r * b/a?
    I think it is safer to derive than to just cite the result formula.
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    Re: Greatest Term

    It's usually 3 marks so derive but check with formula
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    Re: Greatest Term

    Marks are given for the derivation, so it would be best to derive the ratio everytime
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    Re: Greatest Term

    1 out of 3 at best if you use that formula.

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    Re: Greatest Term

    The formula only works for simple single expansions. If you were to find the greatest term of something more complicated like (3+x)n+(1+2x)n you can't exactly use the formula. However, the principle of finding the largest value of k such that T(k+1)>T(k), where T(k+1) is general term of the entire expansion, is still valid (it will just look very different to your standard case).

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    Re: Greatest Term

    Quote Originally Posted by Trebla View Post
    The formula only works for simple single expansions. If you were to find the greatest term of something more complicated like (3+x)n+(1+2x)n you can't exactly use the formula. However, the principle of finding the largest value of k such that T(k+1)>T(k), where T(k+1) is general term of the entire expansion, is still valid (it will just look very different to your standard case).
    In fact there was a past Ext 2 question requiring that method which had nothing to do with the binomial theorem. I think it involved exponentials.

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