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bump, is it possible to prove the result above if its even true?

Re: HSC 2013 3U Marathon Thread Good question, I will post my solution if no-one has solved in by tomorrow.

Re: HSC 2013 3U Marathon Thread How so? :s I know I can't go all out like I can in the 4U Marathon.

This is related to the current problem at hand, but I won't explain my question in case it turns out to be stupidly wrong: Conjecture: f(\theta) = \frac{1}{2}\sum_{k=0}^{n} \binom{2n}{2k-1}(-1)^{k-1} \cos^{2n-2k} \theta \sin^{2k-2} \theta Is this true? f(\theta) = J(n) \cdot f''(\theta)...

That was a really good speech

Re: HSC 2013 3U Marathon Thread :| I have a real bad memory.

Re: HSC 2013 3U Marathon Thread Here is my own little proof of the 'famous' identity (its probably similar to others, but I haven't seen any) $Using the identity$ \ \ \ (1+x)^n (1+x)^n = (1+x)^{2n} $Prove$ \ \ \ \sum_{k=0}^{n} \binom{n}{k}^2 = \binom{2n}{n} \ \ \ \ \fbox{3}

Now, education is supposed to build our skills to help with later life, whether indirectly or directly (school doesn't really prepare us directly). Discuss the value of certain subjects in skill building, I suppose the main areas of focus will be English and Maths, but feel free to discuss about...

I'll try, though its hard to do so when aiming really high Better get that deswa1 attitude.

D: I'm screwed if everyone else is doing this

Not even as a single point at the end? To push the essay further?

How useful is it to use Game theory as a point/main 'thesis' for an Economics essay? What if for instance I am able to answer the essay using Game theory, and I do so for half the essay. Is this a good thing?

Re: The p00n thread No it is something. Fawun, if you don't spend y11 properly you will end up like me, with bad studying habits of barely anything, now fighting since I messed up term 1. y11 should be when you perfect the work ethic, don't bludge it.

Not very elegant of a solution there, here is my own alternatively: x^4-x^2+1 = 0 \ \ | \times x^2 x^6-x^4+x^2=0 \\ \\ x^6=x^4-x^2= - 1 \therefore $the solutions of$ \ \ x^4-x^2+1 \ \ $ are among the solutions of$ \ \ x^6+1=0 \ \ \ $with the additional 2 solutions being created when...

Cristiano Ronaldo Fernando Torres (not sure if he is overrated though) The whole Australian soccer team by the Australian people (though some are not that bad)

Re: HSC 2013 4U Marathon cis npi r can cover the whole unit circle, since it satisfies infinitely many values for integers n. That is, u= cis npi r for some irrational r and number n. Now there are infinitely many u, such that |u-z| < c So it must follow that there is an infinite number of...

Re: HSC 2013 4U Marathon Well I was quite sure so I put it there. It is the converse argument from the first part. The first part says that there are finitely many values if and only if r is rational Conversely, there are infinitely man values if and only if r is irrational. This is the...

Re: HSC 2013 4U Marathon $Let$ \ \ I_{n} = \int_{0}^{\pi} \sin^n x \ dx $i) Prove that$ \ \ \ \frac{I_{n}}{I_{n-1}} = \frac{n-1}{n} \ \ \ \ \fbox{2} $ii) By using the above result twice at least, or otherwise, prove that$ \prod_{n=1}^{\infty} \left (\frac{2n}{2n-1} \cdot \frac{2n}{2n+1}...

Re: HSC 2013 4U Marathon I fixed the wording for my answer to part (i) (ii) $for$ \ \ c>0 Establish the fact that there will always exist some complex u |u|=1 , such that: |u-z| < c \ \ \ $for$ \ \ c>0 There are an infinitely many u such that this condition is true, for ANY z. Now...

Re: HSC 2013 4U Marathon Hahaha biggest failure ever on my part :/