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Re: HSC 2013 4U Marathon lol.

Re: HSC 2013 4U Marathon Obviously :).

project m: demo 2.5.

Re: HSC 2013 4U Marathon I think he meant fishy in the sense that there is unlikely to be an mx2 level solution to this question. If there is, the person who finds it should probably spend his time sending his solution to the Clay Institute rather than typing it here.

Re: HSC 2013 4U Marathon Yes, a solution to this question would be equivalent to proving Riemann.

Re: HSC 2013 4U Marathon Here is a polynomial question that is a past IMO question. Don't let that scare you though as it is from a while ago and is certainly do-able by a good mx2 student. Prove that the solution to the inequality: \sum_{k=1}^{70}\frac{k}{x-k}\geq 5/4 is the union of...

Re: HSC 2013 4U Marathon There is not one in terms of elementary functions.

Re: HSC 2013 4U Marathon Agreed. You would need something like the mean value theorem to actually prove convergence of the taylor series though.

Re: HSC 2013 4U Marathon Same issue though, you would be trying to prove that the infinite series converge to e,sin,cos respectively. But to talk about this happening on C we need to define e,sin and cos on C in the first place!

Re: HSC 2013 4U Marathon I know what a taylor series is, I was asking what you are trying to prove about this infinite sum?

Re: HSC 2013 4U Marathon Well what do you mean by "proving the taylor series formula"? Also power series don't have to converge.

Re: HSC 2013 4U Marathon Well of course not, because it is proving a statement about an object that is not even defined in mx2 (the complex exponential). It is much more convenient to define the trig and exponential functions via power series, whence Euler's formula is a triviality.

Re: HSC 2013 4U Marathon Originally Posted by bleakarcher Hey seanie, just a question. Would you consider this a satisfactory proof of Euler's formul? I remember reading somewhere it's like a poor man's proof of it lol. Let f(x)=cos(x)+isin(x) Consider...

Re: HSC 2013 4U Marathon This is not legit though, as I have explained on these forums before.

Re: HSC 2013 4U Marathon Couldn't find a non-bashy solution to ii), will leave it for Sy to finish :).

Re: HSC 2013 4U Marathon $i) For each positive integer $k$, the number of ways of choosing $k$ fruits out of our $5$ types is \\ $\frac{(k+4)!}{k!4!}$\\ by counting strings consisting of $k$ dots and $4$ dividing slashes.\\Hence the number of ways of choosing some nonzero quantity of fruit at...

That said, it should not be to the extremes of olympiad. There is a sizable difference between contests and exams, and so there should be.

I think to truly assess mathematical understanding/ability, shorter (in terms of number of questions) and more difficult exams would be ideal. Especially for differentiating the top end of the cohort. The board would NEVER go for this though.

Lol. Even the proof of the fundamental theorem of arithmetic is a bit beyond the expectations for mx2 students. The uniqueness part is a little subtle for high school material. (Try proving it on your own if you haven't read a proof before, it is still definitely doable yourself).

Well creativity is the antithesis of rote learning :). Of course there will be some memorisation involved, even an artist or musician relies on memory to build his intuition for what will look/sound good in a particular landscape. The fact that you experiment with mingling bits from different...