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HSC 2013-14 MX1 Marathon (archive) (3 Viewers)

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Sy123

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Re: HSC 2013 3U Marathon Thread

I found a mistake in my working out for the RHS

If i equate coefficients of x^(2n) for [3], i get
I'm pretty sure you get

The n+1th term in that binomial expansion in [3] is
 

JJ345

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Re: HSC 2013 3U Marathon Thread

I don't think so, I could be wrong but I'm getting what the question sasys.
I'm not getting the +g either for some reason. How did you solve it?
 

Sy123

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Re: HSC 2013 3U Marathon Thread

I'm not getting the +g either for some reason. How did you solve it?
Yep I redid and you are right if we take range as distance from projection (which is probably the more correct definition), I took range as distance from origin.
 

Kustom-

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Re: HSC 2013 3U Marathon Thread

OMG I need help with this stupid question -_-

Prove:
sin(x) + sin(nx) = 2sin (nx/2 + x/2) x cos(nx/2 - x/2)

Please!!
 

Carrotsticks

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Re: HSC 2013 3U Marathon Thread

Start with RHS then expand then prove LHS.
 

Kustom-

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Re: HSC 2013 3U Marathon Thread

see I tried but didn't get toooo far... Im not sure how to expand 2sin(x/2) x sin(x/2) x sin(nx/2) x cos(nx/w)
 

Makematics

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Re: HSC 2013 3U Marathon Thread

argh so tempting to use 4U sum to product rules for that haha
 

Sy123

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Re: HSC 2013 3U Marathon Thread





 

Kustom-

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Re: HSC 2013 3U Marathon Thread

nope, im not sure they are correct haha.. i expanded too 2sin(nx/2)cos(x/2) + cos(nx/2)2sin(x/2) x cos(nx/2)cos(x/2) + sin(x/2)sin(nx/2)
then from there did 2sin(nx/2)cos(nx/2) x cos(x/2)Cos(x/2) and got sin(nx)cos^2(x/2) and left with c0s(nx/2)2sin(x/2) x sin(x/2) sin(nx/2)
 

Sy123

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Re: HSC 2013 3U Marathon Thread



 
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Menomaths

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Re: HSC 2013 3U Marathon Thread

Imagine Sy's been getting other people to do his homework for him
 

Sy123

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Re: HSC 2013 3U Marathon Thread

Are you missing an m/(1!) ? (I don't know - I haven't done the question. But it looks like a term is missing.)
I got that question from Summation of Series - Jolley, series number 196.
I'm pretty sure the 1 cancels out which is why it's there

EDIT: Let me redo it I may have made a mistake

Imagine Sy's been getting other people to do his homework for him
hahahahaha
 
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JJ345

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Re: HSC 2013 3U Marathon Thread

I got that question from Summation of Series - Jolley, series number 196.
I'm pretty sure the 1 cancels out which is why it's there
I showed the result but having the m/1! was necessary---> Are you sure there isn't a mistake? I may be wrong though.
 

Sy123

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Re: HSC 2013 3U Marathon Thread

Sorry you are right braintic, I am missing a m/1!, I apologise, fixing now.
 
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