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Re: HSC 2013 4U Marathon Alright then

Re: HSC 2013 4U Marathon T_k \ \ \ $denotes the kth triangular number, which is defined by$ T_k=\sum_{m=0}^{k} m \equiv 1+2+3+...+k $Find the sum$ \sum_{k=1}^{n} T_k \sin k \theta \equiv T_1\sin \theta + T_2 \sin 2\theta + T_3 \sin 3\theta + \dots +T_n \sin n\theta $HINT: You may want...

Re: HSC 2013 4U Marathon lol anything but that ================ I made an easier one now.... $Solve for $ \ \ z 4z^2-16z+30i=0

Re: HSC 2013 4U Marathon Do you have anything difficult to contribute - it would be appreciated

Re: HSC 2013 3U Marathon Thread $By considering the expansion of the RHS$ (1+x)^n = (1+x)(1+x)(1+x)\dots(1+x) \ \ \ \ $(there are an n number of brackets)$ $Prove that$ \ \ \ \ (1+x)^n=\binom{n}{0}+\binom{n}{1}x+\binom{n}{2}x^2+ \dots + \binom{n}{n}x^n

Re: HSC 2013 4U Marathon Well, damn.... lol I give up trying to turn this into a question. (For anyone else, the graph question is still unanswered)

Re: HSC 2013 4U Marathon $i) Show that$ \ \ \ \frac{1+(-1)^{n+1}x^{2n}}{1+x^2} = 1-x^2+x^4-x^6+...+(-1)^ {n-1} x^ {2n-2} \ \ \ \ \ \fbox{0} $ii) By creating an inequality of lower bounds and upper bounds, then taking n to infinity. Prove that$ \tan^{-1}x = x-...

Re: HSC 2013 4U Marathon no problem lol - if you can notice that the thread is dieing then go right ahead. But I think I'm gonna pass on this question

Re: HSC 2013 4U Marathon Another one I made - its original: $Consider the following construction of this particular curve$ Now since I can't draw properly - you must draw it instead, for purposes of this question: $The Red variable point$ \ \ = R $Centre of the moving circle$ \ \ = S...

Re: HSC 2013 4U Marathon Correct - nice work.

Re: HSC 2013 4U Marathon $If $ \ \ P(x) \ \ $ and $ \ \ Q(x) \ \ $are polynomials of degrees$ \ \ m \ \ $ and $ \ \ n \ \ $ respectively. $What is the degree of$ \ \ P(Q(x)) \ \ ? $The polynomial$ \ \ P(x) \ \ $satisfies the equation$ P(P(P(x))) - 3P(x) = -2x $Show that the degree of$...

Re: HSC 2013 4U Marathon It is relatively simple to prove the first result, and yes it is interesting. I actually did try this method with my poly question but it didn't seem to output any encouraging results. And yes they probably are not able to be manipulated into polynomial form, but if...

Re: HSC 2013 4U Marathon Err, not sure what you're talking about :P Only maths here, if that's what you're talking about.

Re: HSC 2013 4U Marathon Nice work, alternatively while we can do it your way, do you see how you needed to find \frac{1}{\alpha}+ 1/ \beta + 1/ \gamma And sum of them two at a time, then three at a time -> why not find a polynomial with roots 1/alpha 1/beta 1/gamma And it actually isn't...

Re: HSC 2013 4U Marathon Well I did have the 3 dots implying that it continued to infinity after the nth term, but I will change it again (even though no-one else will answer it)

Re: HSC 2013 4U Marathon Are a, b, c real? I won't answer it in this thread if I get the answer.

Re: HSC 2013 4U Marathon Yeah something like that, I only remember that the first 2 terms were 2, 3 and co-efficient of x was 0. So yeah good enough lol. How did you do it?

Re: HSC 2013 4U Marathon :( - its probably the questions. And that I answer them too fast not giving a chance for others. Ok, next time someone posts a normal type question I will leave it for others to answer it so the participation rate is too high. So yeah if someone could post a question...

Re: HSC 2013 4U Marathon Correct, good job - and what do you mean by your first sentence lol?

Re: HSC 2013 4U Marathon Yeah, I rephrased it: MkIII