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Re: HSC 2014 4U Marathon Letting, n=2, it should follow from this inequality: \frac{a_1}{a_2} + \sqrt{\frac{a_2}{a_3}} \geq 3 \sqrt[3]{\frac{1}{4}} EDIT: Actually it works my bad!

Re: HSC 2014 4U Marathon Could you clarify what you mean by a_m = a_{n+m} , there is no term in the sum beyond a_{n+1} , so I was wondering if it were perhaps something like a_m = a_{n-m}

Re: HSC 2014 4U Marathon Essentially we must show that the sum cannot be prime. We know firstly p_n > p_{n-1} Therefore, p_n! = p_n \cdot (p_n -1) \dots \cdot p_{n-1}! \ \ \ \ \dots (*) Therefore, p_1! + p_2! + \dots + p_n! = p_1! (1 + k_2 + k_3 + \dots + k_n) Due to, (*), each...

1 - In some cases of private tutoring, tutoring is conducted by students just coming from the HSC, don't let this deceive you, as though they somehow are capable with knowledge. I am willing to bet that only a small portion of students who end up tutoring know content really well, and only a...

Re: HSC 2014 4U Marathon Is it only 1? 1 \rightarrow n \rightarrow 2 \rightarrow n-1 \rightarrow 3 \dots Resulting in: 1 + 2 + \dots + (n-1) = \frac{n}{2} (n-1) Now to prove that this is the only trip possible to yield maximal length: Our initial moves are 1 \rightarrow n This is the...

Re: HSC 2014 4U Marathon \\ $i) Show using DeMovieres that$ \\\\ \cos(3\theta) = 4\cos^3 \theta - 3\cos \theta \\ \\ $ii) Hence solve the equation$ \ \ \ 8x^3 - 6x - \sqrt{3} = 0

Re: HSC 2013 4U Marathon Nice. For the first rough version of the compilation, see the first post, I have edited it in there. ------------- \\ $In the argand plane, the third and fourth roots of unity are plotted on the plane. A square is constructed with the fourth roots of unity, and a...

Re: HSC 2013 4U Marathon Mostly finished, I omitted most of seanieg's questions, I will compile them if I can solve them, if I cannot I will eventually make it a separate compilation for advanced problems. I just need to sort it. \\ $i) Expand$ \ \ (1+\cos \theta + i\sin \theta)^3 \\ \\ $ii)...

Re: HSC 2013 4U Marathon Replace the sqrt(2) with 2 and its correct :) The proper way to do it is just consider: f\left(\frac{z}{2} \right) = \frac{\frac{z}{2} +i}{\frac{z}{2} - i} We know that it is purely imaginary for |\frac{z}{2} | = 1 Therefore it is purely imaginary for |z| =2

Re: HSC 2013 4U Marathon Yep for the first it is |z| = 1, not sure how you got to z=+- 1 though, z can be complex as well (for example, as an excercise try putting z=1/2 + sqrt(3)/2 i in that function, it should output a purely imaginary number) For the second one, try thinking of a function...

Re: HSC 2013 4U Marathon I can try to do that

Re: HSC 2013 4U Marathon $For what$ \ z \ $is the complex function$ \ \ f(z) = \frac{z+i}{z-i} \ \ $purely imaginary?$ $Determine the function$ \ g(z) \ $which is purely imaginary for$ \ \ |z| =2 As for an update on compilation process, I'm up to page 63 right now, its a much longer...

Anyone here play Valve's Matchmaking? What rank?

Re: HSC 2013 4U Marathon I took a little (a big) break with it, I'll make sure to get to at least page 40 by tonight and continue regularly from there

Any other input that will make drawing diagrams or even latex documentation easier is appreciated

Thanks for the input!

Thanks for the input!

Its not just English either Pretty much every discipline bar Mathematics, Logic and its derivatives (Computer Science and so on) are the only subjects where ambiguity is eliminated completely I think Even with sciences, no matter how 'rigorous' we are in areas such as Physics, its always up to...

Following on from this (which is an interesting read to say the least): http://www.reddit.com/r/AskReddit/comments/1prbm7/mathematicians_of_reddit_what_is_beautiful_about/ What do you find beautiful about mathematics? For me as a 'laymathstudent', I find things like infinite series...

How do you make diagrams such as those that appear in the HSC? Do HSC papers use MathType or do they use Latex with a different font? Does this matter? Which is easier to use and learn? Thank you