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Let m and n be two positive integers with: m%3E%20n a) Show that: \sum_{r=1}^{n+1}%20\binom{2n+1}{n+r}=2^{2n} b) By considering the coefficient of x^{k} in (1+x)^{m}%20(1+\frac{1}{x})^{n} show that: \sum_{r=0}^{m-k}%20\binom{m}{k+r}\binom{n}{r}=\binom{m+n}{n+k} I know how to do part (a) but...

Yeah, that's right, it is really easy but say in the test you don't realise that 1 + 2 + 3 + … + n = n/2 (n+1), this means you can't do the question.

A and B have (n+1) and n fair coins respectively and they toss their coins simultaneously. a) Show that the probability that B gets r heads is given by: \frac{1}{2^{n}}\binom{n}{r} b) Hence, find the probability that A will obtain k more heads than B, where: 1\leq%20k\leq%20n+1 c) Show that...

Sorry, my bad, it is a factorial :( I was revising complex numbers today so I'm still into imaginary stuff LOL

Carrotsticks, try the harder 3 unit question I posted recently please, I'm interested to see what u can come up with :)

4unit maths ???

2UNIT MATHS IS A JOKE :) IT IS SO EASY. People who did not do Ex1 and Ex2 maths at my school are struggling with 2UNIT Maths because they have very limited knowledge. Ex2 maths helped me a lot, it makes other subjects look so easy, well 4UNIT isn't that hard itself, teachers make it seem hard...

Can you say the ellipse is a circle with longer/shorter radii so area is Pi(a)(b) if it was part of a volume question, i.e. the question doesn't explicitly ask you to prove it or do you have to do through the integration all the time?

2Pac - Hail Mary !!!

The AM-GM inequality states that for any n positive real numbers a1, a2, a3, … an: \frac{a_{1}+a_{2}+...+a_{n}}{n}%20\geq%20\sqrt[n]{a_{1}a_{2}...a_{n}} Prove that: (n+1)^n\geq%202^{n}n! Can anyone prove this? It is really tricky but once you get it is easy to solve.

Feelings are the only things that prevent people from achieving their goals (love, hate, sleepy, hungry, tired, upset, mad, horny etc...) If you forget about these stupid feelings and just work like a machine to achieve your goal, you will achieve it eventually but if you keep thinking "I'm...

Do I still have to do umat if I get 99.95? I'm not sure if im gonna get that, in case I don't, can anyone PLEASE tell me more about gamsat?

Yeah, I asked him today, he said, question 8 won't be as hard in the new format, they are distributing the difficulty but this is not good, many people will do well in this case.

And how come anti matter have negative mass, isn't mass always positive, doesn't make sense either.

I'll try and do all question 8's from 1990 - 2011. Do you think a tutor can help with this type of questions or I have to rely on my own skills?

I have the westone 4R's, best earphones on the market, pretty expensive though, about $400 LOL and that's the cheapest, they are usually $550

Get audio technica M50, best value, an awesome headphone for $125 sennheisers in another option never ever get celebrity endorsed crap like beats.

What about doctors who do MRI's at hospitals and doctors who do physiotherapy and doctors who do/analyse x-rays, sonar, ultrasound ... imaging, im pretty sure they are doctors. and they never touch human organs, they just work with machines. idk, I'm just thinking about what u can possibly do...

You still can do medical physics, i.e. design and use medical machines etc... cant you?

I'm not doing UMAT but, so I have to do GAMSAT. I thought doing science will help me ace the gamsat.