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HSC Mathematics Marathon (1 Viewer)

largarithmic

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Nice, I did pretty much the same thing ^^ I think you can motivate it by (1) knowing you want to somehow telescope, and (2) after computing a few values you guess that it goes to 3. Which would make sense as one on a third, so you try telescoping with 1/un.

Telescoping means that technique to sum a sequence: if you want to find sum un, you find some sequence sn s.t. un = s_(n-1) - s_n, then when you add them up, sum (1 to n) u_k = s_0 - s_n, which is often easy to compute.
 

largarithmic

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so is this an olympiad question?
It could possibly be an easy olympiad question. The difference between easy olympiad questions and hard "harder 3U" questions is almost nil though. The entire circle geometry topic, entire probability topic, most induction questions (probably not those involving trig functions), definitely all 'inequalities' and most miscellaneous 'sequence' questions like this could be considered as 'olympiad questions'
 

cutemouse

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And why is it a stupid question, because it's unconventional?
No, because firstly, in that year many students who were involved with various maths clubs had seen that question before and therefore could do it easily. Whilst those who hadn't seen it before couldn't do it.

And it doesn't really test the course IMO.
 

apollo1

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i thought you were talking about q8 2010
lol no. i havent done any hsc papers yet. im saving them until the first week of october. doing independent trials atm.
 

hup

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lol no. i havent done any hsc papers yet. im saving them until the first week of october. doing independent trials atm.
if you look theres solutions at the back but it is wrong
x by vector = rotate anticlockwise not clockwise
 

apollo1

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if you look theres solutions at the back but it is wrong
x by vector = rotate anticlockwise not clockwise
ooh didnt no there was solutions. the solutions look right. wat do u think is wrong wit it?
 

hup

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ooh didnt no there was solutions. the solutions look right. wat do u think is wrong wit it?
they are saying that CA = wCB, which is wrong
eg
if you have p=iq, then p =cis(pi/2)q so you are rotating vector q 90 deg anti clockwise
so it should be CB = wCA
 

apollo1

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wat if you produced vector CA at C. then if you rotated vector BC 120 degrees anticlockwise it would turn into vector CA giving you desired result. is this valid?
 

hup

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wat if you produced vector CA at C. then if you rotated vector BC 120 degrees anticlockwise it would turn into vector CA giving you desired result. is this valid?
actually its my bad I thought it was pi/3 not 2pi/3 yes solution is valid
 

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