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March 29, 2024, 08:50:00 am

Author Topic: Binomial Theorem 2014 HSC QUestions  (Read 3540 times)  Share 

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callumliasides

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Binomial Theorem 2014 HSC QUestions
« on: August 09, 2016, 02:29:46 pm »
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I am terrible at binomial theorem and this question, even part a is going straight over my head do you mind if could grab some help, it would be greatly appreciated, thank you :)

callumliasides

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Re: Binomial Theorem 2014 HSC QUestions
« Reply #1 on: August 09, 2016, 02:35:57 pm »
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Also I apologise i didnt realise I had made a new topic! and it seems I can't delete the post haha :/

jamonwindeyer

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Re: Binomial Theorem 2014 HSC QUestions
« Reply #2 on: August 09, 2016, 02:39:35 pm »
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I am terrible at binomial theorem and this question, even part a is going straight over my head do you mind if could grab some help, it would be greatly appreciated, thank you :)

Hey Callum! Welcome to the forums!! Let me know if you need help finding anything ;D

I have to head to a lecture in a minute so I won't do the whole question yet, but Part A comes from the definition of a combination!




I'll give you a hand with the rest tonight (assuming someone else doesn't tag in to give you a hand first)  ;)

Also I apologise i didnt realise I had made a new topic! and it seems I can't delete the post haha :/

No dramas at all! New thread means we can help you without other posts breaking the flow ;D

Quick Hint for the 2nd One While You Wait: Consider:



The coefficient of x^n on the left hand side will be equal to the function f(r)! (can you see how this happens if we expand?)

But the coefficient of x^n must be the same on both sides, what is it on the right hand side? ;D
« Last Edit: August 09, 2016, 02:42:22 pm by jamonwindeyer »

jamonwindeyer

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Re: Binomial Theorem 2014 HSC QUestions
« Reply #3 on: August 09, 2016, 09:22:27 pm »
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Hey! Okay, so for that second question, as I alluded, you are equating coefficients:



We seek coefficients of some random term, x^r. On the left, we are pairing off terms which will multiply to give a power of x^r, for example, the coefficient of x^r will pair with a constant term. The coefficient of x^(r-2) will pair with the coefficient of x^2 in the other bracket. Etc. Taking these product of these coefficients gives one side of the relationship in the question. The other side falls straight out of the RHS, by considering the coefficient of x^r.

The bottom one stumped me for a bit, but it is similar! The RHS suggests that we consider the following identity:



This time, we are considering coefficients of x^n.





We apply this logic to all the pairs in the LHS of the relationship, and by equating coefficient, the result comes out!

This is a really tricky one to explain, a super tough question. Read this a few times, work with me if you can, see if you follow my reasoning, and of course ask any questions you might have ;D

RuiAce

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Re: Binomial Theorem 2014 HSC QUestions
« Reply #4 on: August 09, 2016, 09:58:34 pm »
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I am terrible at binomial theorem and this question, even part a is going straight over my head do you mind if could grab some help, it would be greatly appreciated, thank you :)





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callumliasides

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Re: Binomial Theorem 2014 HSC QUestions
« Reply #5 on: August 09, 2016, 10:09:00 pm »
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Thank you so much!!! I figured out part a) just a bit after I posted the question, but part iii) had me stumped! i really appreciate the help :)