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Re: HSC 2015 4U Marathon - Advanced Level Note that there are an ODD number of terms in (z+1/z)^(2n). That is why the 2nCn is there in my work and there isn't just a division by 2. Also note that my 2n is your n. I wrote it that way to incorporate the even condition immediately.

Re: HSC 2015 4U Marathon - Advanced Level No, you certainly can't. Otherwise suppose the equation is true for a given n and for any c and any theta. Then by setting (theta,c)=(0,1) and then (theta,c)=(0,2), we are able to use these two equations to deduce that 1=2. As far as I know, 1 does...

Re: HSC 2015 4U Marathon - Advanced Level Using standard complex numbers tricks (raise a complex number on the unit circle plus it's reciprocal to the power 2n in two different ways) and exploiting that cos is even we can write the RHS as: \frac{1}{2}(\binom{2n}{n}+2^{2n}\cos^{2n}(\theta))+c...

Re: HSC 2015 4U Marathon - Advanced Level Can you also elaborate on the RHS using some kind of summation notation? It is not clear what fills the "..." given that there are cosines at the start but not the end.

Re: HSC 2015 4U Marathon - Advanced Level How did you deduce that in a group with no-one beating anyone else all the scores must be equal? Eg AAAAB doesn't beat BBBBA despite having a wayy better score.

Re: HSC 2015 4U Marathon - Advanced Level A school offers 8 subjects in year 12, all of which are compulsory. For each subject, each student either receives an A or a B. We say student 1 beat student 2 if every grade of student 1 is at least equal to the corresponding grade of student 2 and...

Re: HSC 2015 4U Marathon I got 84, form a string of 6 slashes 3 dots etc.

Re: HSC 2015 4U Marathon The common ration has modulus 1, so this is not a convergent series. Using the infinite geometric series formula here is meaningless.

Re: HSC 2015 4U Marathon Yeah, quite sure 30 is correct.

Re: HSC 2015 4U Marathon Neither of you confirmed his guess or corrected my post "well, the first (k+1) of them anyway". I am not trying to be mean or anything, I'm just trying to impress on you the importance of certainty when it comes to making your own questions. People won't want to...

Re: HSC 2015 4U Marathon The issue was not so much difficulty as you not saying that: a) k=n-1 b) n is even. b) is not a big deal, but a) certainly is. I still don't think that the question (as originally posed) is doable.

Re: HSC 2015 4U Marathon I only ask how sure you are because of how often I see people (especially students) make up their own questions that don't work. Hopefully (mostly for the sake of students time) this is not such a question, but I am still a little doubtful that you will be able to...

Re: HSC 2015 4U Marathon well, the first (k+1) of them anyway.

Re: HSC 2015 4U Marathon Er, are you really sure you have a nice expression for this? I am a bit sceptical. You should probably phrase it as a "prove that ..." question so people can easily check that the question works before spending time on it.

Re: MX2 2015 Integration Marathon Yeah for negative reals, the principal square root is just an imaginary number with positive imaginary part. More generally, the principal argument of a complex number z is the argument in the interval (-pi,pi]. (Note that any complex number will have at least...

Re: HSC 2015 4U Marathon - Advanced Level bump.

It's better than brawl but still pretty snoozetastic, especially to watch. But for people who are only getting into smash starting with 4, watch: Did anyone else catch Apex 2015? It was very hype.

Kirby nerfed? Lol Kirby is trash in melee.