Dave

It should come out from the method I've stated, but I may have made a silly error somewhere. If I have time later, I'll work through it.

Nope, but when I was shopping around for calculators for uni, I thought "what the hell, I may as well get the more expensive calculator because it does more". If you're going to fork out quite a bit for a ti-83, then you may as well go the whole way and fork out a little more for a ti-89. Plus, it is a brilliant calculator. But it doesn't make you a lot better at maths.

It wouldn't surprise me. Microsoft at its best again

In regard to the actual theory itself, I'm not going to comment too much because this is way out of my area of knowledge. It sounds like you've put some thought into it, but you'd need to do a fair bit of heavy duty maths to get some sort of idea whether you're along the right lines.

A quick google gave this: http://www.sciencenet.org.uk/database/Physics/9701/p00540d.html

It's not the fact that he's wrong that disturbs me. It's the fact that after all this time and scientific explanation, he's still spouting the same old crap and refusing to believe it's wrong. Then again, teh bit with the humans and homo-sapiens is quite funny tbh.

Well I've decided to post the answers because I don't want to leave people hanging in the loop but I'll put another question up tomorrow or the day after (or when I have time). Any suggestions should be mailed to me. Cheers mathssol2.pdf

I rarely use my ti-89 apart from checking I have the right answers. In general, I don't really use a calculator at all apart from working out values for sin, sqrts, etc.

Nobody's actually posted anything yet, so I'll give you all a bit more of a chance before posting the answers.

same here.

For the graph y=sin(4x), over a range 0 -> 2*pi of x values, you can say that there are 4 ordinary sine curves, but they are all crammed together in the space where there would only be one. If you're going to take a quarter of this range, then clearly the area underneath this quarter is going to be equal to the area underneath one of these crammed sine curves, which will be zero.

deep down it's in all of us

It may be that there is a universal reference frame, but we don't have the science/technology to prove/detect it.

I find the questions incredibly annoying, tedious and of no real use whatsoever to be honest. At the end of the day, it might broaden your knowledge of being able to interpret a question and perhaps a bit of lateral thinking, but it won't really help your mathematics in an extreme way.

Also, notice that after x is bigger than about 5 or so, the term 7^(-x) is so small you can just ignore it. From my calculator, 7^(-20) = 1/79792266297612001, which is pretty small. It also managed to work out your answer exactly which was quite impressive, but it's so large that I couldn't be bothered typing it out. (I have a TI-89, which is just the best calculator ever. I used it to check my series.)

Incidentally, I've moved the thread over the number theory forum which is more appropriate for this.

In fact, it's dead easy. f(x) = x*sum(r=1->x) 7^(-r) = x * ( sum(r=1->inf) 7^(-r) - sum(r=n+1->inf) 7^(-r) Basically, I've split the sum up into 2 seperate infinite series because the series is obviously going to converge and it's a geometic progression. This makes the task pretty simple. I also took an x out because it's a common factor. We also know that S (sum of infinite geometric series) = a/(1-r), where a is the first term in the series and r is the ratio between any two terms in a geometric series). Therefore f(x) = x*(1/6 - 7^(-x)/6) Put the numbers in and it works pretty nice. I've missed out a load of explanation, but there's your general solution.

This is why I hate mensa questions. Can't think of a way to sum that series offhand, I'll have a look at it though.

From the question, surely the answer is 679/7 or am I missing something?

On a completely separate point, what do you think of the current education system in Britain as regards to examinations? For people who are outside Britain, it basically goes like this. You get exams when you are 7, 11, 14 and 16. Then, if you decide to do your A-levels (which get you into university) then you have to do exams when you're 17 and 18, which is, in total 6 sets of examinations. In my opinion this is far too much, and the teachers are right to boycott some of these examinations, because at the end of the day they're not going to have time to teach the kids what they need for life, but what they need for the exams. Also, I think the old A-level scheme was a hell of a lot better than bringing in separate AS and A2 level examinations, which are just pointless.

Take a look at this. I can see where he's coming from, but personally I think that perhaps there should be a choice between a more applied mathematics GCSE and a full mathematics GCSE. One should be compulsory, because pupils definately need some basic mathematical skills.

Is anyone else finding the rapid infection rate in China a little worrying? Along with the news that it can mutate rather rapidly I'm pretty concerned now.

Sounds good to me. I'm all for a bit of light entertainment.

I'd better get started then

I really am quite looking forward to this, since it means that when we all get fried by the cosmic radiation, I won't have to do any revision for the damn a-levels that are coming up.