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Thanks for the tip, zhiying.

Haha I was thinking of that. That's how I got the idea behind my solution.

No worries lol; one of these days, I swear I will learn LaTex. Now I was wondering about the actual series in question, do we actually get the same result by summing each G.P. together? Or do we get another expression, and does it also tend to infinity? If they are different, which one 'grows'...

Alrighty, brace for a complete mess; I have no idea how to use LaTex. let S = x + 2x^2 + 3x^3 + ... + nx^n now, xS = x^2 + 2x^3 + 3x^4 + ... + (n - 1)x^n + nx^(n+1) subtracting xS from S, we get S - xS = x + 2x^2 + 3x^3 + 4x^4 + ... + nx^n - (x ^2 + 2x^3 + 3x^4 + ... + (n - 1)x^n) - nx^(n+1)...

Well, I never really discussed these kind of things in front of my classmates. My teachers just got sick of me asking questions before and after a lesson, and during lunch. So now I just look up what I want on the net. Now back to Fus Ro Dah's question, would the value of the integral be the...

Hot diggity, my Maths test is pushed back a day!

Fortunately, I have improved somewhat in that regard... I shut up now. Besides, now I just tell silly stories of my various adventures, people tend to like them more.

I can't be the only one who has/had their teachers tell them to shut up in class because they were rambling on and on about tertiary-level maths.

Thanks man, I'll have a look for it.

Ahh, of course. I forgot about turning it into a sec-based problem, but I am unfamiliar with the relationship between integration and convergence/divergence. I was too busy trying to think of some way I could express this new integral in terms of the original. I wish this damn HSC would hurry...

Sorry, I meant for replacing the exponent of the cosine in the integral, with a negative. I was thinking about it because for part i. of the solution, as using a negative would result in cos(-2ntheta), which could be rewritten as cos(2ntheta) I've heard about using the gamma function to do...

It helps having a past paper book within arm's reach lol. Now, what happens to the integral in question for negative numbers? Although de moivre's theorem extends to negatives, I'm assuming the binomial expansion is radically different (if it exists)

Ha! I found it. It was Q7 b from the '09 paper.

Wasn't this a past paper question? If I remember what i did the first time i tried this question, for carrotsticks' method #2, you go and prove: i. z^n + z^-n = 2cos(ntheta) by de moivre's theorem & some manipulation ii. use this to then expand (2cos(theta))^2n = some binomial mess...

http://community.boredofstudies.org/showthread.php?t=267778 Worked solutions to New Senior Mathematics (aka fitz)

What? 5AM starts or is that just when you have to wake up?

I'm jealous. I want to do as much maths as possible.

My class is finishing up Complex numbers next week (I think we just have a bits and pieces to learn) and we are starting Graphs later next week. We have 3 lessons a week.

Adv English : haven't got it yet lol EX1: 83%, 1/4 Adv Math: 88%, 2/14 MX1: 77%, 1/7 Chemistry: 89%, 1/~24 Physics: 61%, 1/14 Biology: 79%, 1/~50 School rank: ~580 lol Overall: Fail. My school used the Independent papers for everything. I'm gunna get destroyed in the HSC... but at least MX2...