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Thread: Ratios of Binomial Expansions

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    Cadet Heresy's Avatar
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    Ratios of Binomial Expansions

    1) In the expansion of (1+x)^16, fing the ratio of the term in x^13 to the term in x^11.

    2) In the expansion of (2+3x)^n, the coefficients of x^5 and x^6 are in the ratio 4:9. Find the value of n.

    Any help would be great, thanks!
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    Re: Ratios of Binomial Expansions



    We want to find the terms in and .

    These are:



    Ratio:



    Note that the ratio should be less than 1, because for raised to any power, the coefficients will be largest in the "middle" of the expansion.

    The expansion for 2) will be



    You are given that the ratio of the co-efficients of and is .

    Can you take it from here?
    Last edited by fan96; 3 Nov 2018 at 3:07 PM.

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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by fan96 View Post


    We want to find the terms in and .

    These are:



    Ratio:



    Note that the ratio should be less than 1, because for raised to any power, the coefficients will be largest in the "middle" of the expansion.

    The expansion for 2) will be



    You are given that the ratio of the co-efficients of and is .

    Can you take it from here?
    I should be able to;
    When you simplify 16C13/16C11 and change it into factorial notation - how does the 5! and 11! get on the denominator while 3! and 13! get on the the denominator? Sorry if its a dumb question - just need an explanation please.
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    Re: Ratios of Binomial Expansions



    Sometimes if you have nested fractions they can be very confusing.

    Another way to think about it is to multiply both the numerator and denominator by .

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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by fan96 View Post


    Sometimes if you have nested fractions they can be very confusing.

    Another way to think about it is to multiply both the numerator and denominator by .
    Yeah - Thank you so much.
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    Re: Ratios of Binomial Expansions

    Even though fan96 ninjad me lol



    Last edited by HeroWise; 3 Nov 2018 at 5:54 PM.
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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by HeroWise View Post
    Even though fan96 ninjad me lol



    Thank you so much
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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by HeroWise View Post
    Even though fan96 ninjad me lol



    Hey HeroWise, the answer is apparently 14 for this one - idk why - the working out looks fine to me (The question is from 5D in Cambridge 3U Year 12)
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    Re: Ratios of Binomial Expansions

    I redid it im still gettign 9 i think text book errata

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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by HeroWise View Post
    Even though fan96 ninjad me lol



    Quote Originally Posted by Heresy View Post
    Hey HeroWise, the answer is apparently 14 for this one - idk why - the working out looks fine to me (The question is from 5D in Cambridge 3U Year 12)
    Quote Originally Posted by HeroWise View Post
    I redid it im still gettign 9 i think text book errata
    HeroWise likes this.

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    Re: Ratios of Binomial Expansions

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    Re: Ratios of Binomial Expansions

    oml I just realised, what i did there lol ill fix it asap. Was probs high while doing it lolll
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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by InteGrand View Post
    Thanks for the tip!
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    Re: Ratios of Binomial Expansions

    Quote Originally Posted by HeroWise View Post
    oml I just realised, what i did there lol ill fix it asap. Was probs high while doing it lolll
    Haha. Thanks for helping anyways - really appreciate it!
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