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Re: HSC 2013 4U Marathon $Find (with careful proof) \\ \\ $\lim_{n\rightarrow \infty}\sum_{k=0}^n {n\choose k}^{-1}$. $

Bring it ;).

Re: HSC 2013 3U Marathon Thread Good question!

Re: HSC 2013 3U Marathon Thread Hence prove that \frac{d}{dx}\left(x^r\right)=rx^{r-1} for all rational r.

Re: HSC 2013 4U Marathon I don't want to be shown up by any current MX2 students :P. Haha yeah, I recognised it, although I forgot the way the question guided you through it (I did my HSC in 07). P.S. Obviously, I would supply some intermediate reasoning in an actual exam haha.

Re: HSC 2013 4U Marathon P=\frac{n^2}{\sum_{k=1}^n d_k}=\frac{n^2\sin\left(\frac{\pi}{n}\right)}{\sum_{k=1}^n \sin\left(\frac{ k\pi}{n}\right)}=\frac{n^2\sin\left(\frac{\pi}{2n}\right)\sin\left(\frac{\pi}{n}\right)}{\sin \left(\frac{(n-1)\pi}{2n}\right)}\rightarrow \frac{\pi^2}{2}.

Oh I just realised that it's midweek, I am actually unlikely to be able to make it in that case. Can I get a digital copy on like the evening you run the test though so I can put myself through it in exam conditions or something?

Re: HSC 2013 3U Marathon Thread 5!/(5^5)=24/625.

:(

Haha sweet.

Can I do it for fun if in Sydney? Am probably pretty slow these days though.

Re: MX2 Integration Marathon But in the initial integration, a=0 means that you are integrating over an interval of length 0, of course this will give you 0.

Doing a mass amount of questions is a much less effective (and imo infinitely less fun) way of developing understanding than doing fewer harder questions slowly and really analysing your thought processes afterwards. There is a lot more to understanding a particular concept than learning the...

Re: HSC 2013 4U Marathon Yeah, definitely one of my favourite puzzle type questions. It's been proven relatively recently that that strategy is actually optimal, but that is MUCH harder I think.

Re: HSC 2013 4U Marathon If each student was allowed to open boxes indefinitely, as directed by the contained pieces of paper, he would eventually have to open a box he already has opened (as there are only finitely many boxes). As each box can only have one piece of paper pointing to it...

Not if you are learning uni maths properly. So many things in high school (especially calculus) are super nonrigorous.

Re: HSC 2013 4U Marathon Sure, will do so tonight.

If you do it correctly then no. Similarly, when you analyse banked tracks and other higher dimensional systems you can choose whatever coordinate axes you like. (Well any coordinate axes that are inertial of course.)

Re: HSC 2013 4U Marathon Good effort, from a skim read it seems some of the ideas are there. I will try to wrap my head around your notation a little more carefully later to see exactly what's going on, but something is going wrong because your expression is something like 0.99996 for...

Re: HSC 2013 4U Marathon Hey, nice. This is pretty much what I had in mind. There are actually non-hyperbolic solutions if we drop (iii), such as any line of the form ax+by=c (a,b,c > 0): the tangent at any point will be the line itself, so the constant area property is trivial. We could...