Ratios of Binomial Expansions (1 Viewer)

Heresy

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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!
 

fan96

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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?
 
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Heresy

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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.
 

fan96

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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 .
 

Heresy

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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.
 

Heresy

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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)
 

HeroWise

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

HeroWise

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oml I just realised, what i did there lol ill fix it asap. Was probs high while doing it lolll
 

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