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Alright awesome (or not awesome), is it possible for us to know the full mark out of 100? (or do I have to wait another whole year lol)

Since I accelerated MX1 I got a mark X/50 However I will be doing MX2 and hence MX1 will be counting for 2 units, and hence my mark doubles. So would it become: 2X/100 ? And thence my mark will always be an even number? (this is significant for me, I need to know)

-edit- check pm

Re: HSC 2013 4U Marathon Ah yeah that makes sense. Technically we could find an inequality like cot x < 1 / x to but instead cot x > f( x ) to create an upperbound right?

Re: HSC 2013 4U Marathon Nope, CSSA Q16 was a real finding the Basel Problem rather than just the expression in this case. Though for the result at the end of Heroic's question, I have a question for the maths pros If I take the limit to infinity of the RHS of Heroic's last result. I get the...

Re: HSC 2013 4U Marathon I cant be bothered writing the whole sequence out for each theta, so I will do this: Let \theta_k= \frac{k\pi}{2m+1} \cot^2 \theta_1 + \cot^2 \theta_2+...+\cot^2 \theta_m= $something$ \cot^2 \theta_k < 1/\theta_k^2 1/\theta_1^2+1/\theta_2^2+...+1/\theta_m^2 >...

Re: HSC 2013 4U Marathon Good question, I'll type necessary details: a) (\cos \theta +i\sin \theta)^{2m+1} = \binom{2m+1}{0}\cos^{2m+1} \theta +... Equate imaginary parts and the solution falls out. We get the last term as (-1)^m as i^(odd) will either be -i or -1. And since we equate...

Re: HSC 2013 4U Marathon Heroic your reasoning for the why it is (-4)^n is wrong but all up until the last part is right. Rethink what it means whether n is odd or even. I will do your question now.

Re: HSC 2013 4U Marathon Alright thanks guys

Re: HSC 2013 4U Marathon Yes this is what I intended but it seems that the roots do not work.... Can a math pro please explain why this is the case?

Re: HSC 2013 4U Marathon That is one case of it, yes. I should of extended the question to: $Find the possible roots of S(x)$ So yeah consider if -1 is the first or the last term etc.

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Re: HSC 2013 4U Marathon Just in case other people did not see it.

Re: HSC 2013 4U Marathon Oh I see, nice solution.

Oh that is pretty cool. Nice. But can we generate something like this for transcendental numbers, do they require something more complicated, the only examples that were given involved square roots which are not transcendental. With the exception of, for example: \sum_{n=1}^{\infty}e/2...

Re: HSC 2013 4U Marathon Something a little easier: $Given the polynomial$ \ \ \ S(x)=Ax^3+Bx^2+Bx+A $The roots are in arithmetic sequence$ $Hence find the roots$

Re: HSC 2013 4U Marathon iii) Not sure how to actually deduce it from previous results but I can easily evaluate both sides. LHS is a telescoping sum from which we get: \lim_{k \to \infty}1-\frac{1}{k+1}) = 1 RHS is a limiting sum of a geometric series: RHS=\frac{1/2}{1-1/2}=1=LHS iv)...

Parametric equations are used in calculating Projectile Motion, which by itself has a whole range of uses. They can help us define things respective to time much easier. Which would help I imagine in areas such as engineering

Re: HSC 2013 4U Marathon Oops, well I'll fix that now. Thanks

I don't really take notes in class at all. Well my teacher doesn't really, sometimes its just a brief one line theorem statement, or something. Then following that is just examples of questions under that topic that we do in class. Then from there its just practise, and this has helped me very...