Dave

Whilst it's certainly true that [math]\int x^n \ dx = \frac{x^{n+1}}{n+1} + c[/math] (assming n not equal to -1), you can't do this for things like xx - we're assuming that the n in the first equation is constant.

That's because it can't be integrated Not every function is integrable.

Since this has turned into insult flinging, I'm going to close the thread. Grant, your refusal to observe basic English only serves to diminish what little respect other forum members have for you. There is no excuse for not using proper grammar and punctuation, especially when you are taught it from a very early age. I would suggest that you take on board some of the advice given to you in this thread.

I should also mention that identifying periodic decimals is, to some degree, a tricky endeavour. For example, how are you meant to represent an infinite decimal? If you input something like 5.142857142857142857 as you've done above, then this is a terminating decimal. For an infinite fraction, you're much better off by allowing some sort of input such as 5.142857... or 5.142857. By doing this, it allows the user to distinguish whether they actually want to input a repeating decimal or just a plain old terminating one. Also, it makes it a lot easier for you, the programmer, to identify things such as the period or delay of the decimal.

I don't know of any mathematical methods for doing this, but it should be reasonably okay using some programming techniques. I would suggest reading your number in from the textbox as a string instead of a double (I presume that's what you're doing at the moment).

Not usually, no. However, people had already posted complete solutions before I had a chance to survey the thread, so I couldn't really do much about it then.

Well, you've got the correct method - I can't see a more optimized version, myself. Identifying and simplifying the fraction is a fairly simple process. If you have a periodic fraction and you're given what that is (i.e. you don't have to identify it from a string), then the fraction can be worked out in one step. Moreover, Euclid's algorithm can be used to find the fraction in its lowest terms. There are more efficient versions of Euclid's algorithm, but nevertheless, I would say that this method is more than sufficient for most applications.

You can put environmental posts in the Earth Sciences forum. We don't really have a technology forum as such, but you could probably post those things in the Engineering forum.

I feel that I should probably chip in here, since a lot of this falls under my purview. However, a lot of what I want to say has already been mentioned. I would just hope that people understand that this was by no means a "spur of the moment" thing - after all, Johnny5 racked up in excess of 1,500 posts at his stay on SFN. Whilst he did make some interesting points on a variety of topics, in general his posts were all about proving some established theory or concept wrong - that is not what these boards are all about. I and other mods have already checked this; without meaning to cause alarm of offense to Thomas Kirby, it is something we do quite a lot. However, there is not one iota of evidence to show that they are "obviously" the same person. Please don't make unsubstantiated claims in public; if you wish to raise an issue with someone, do it in PM.

Oh come on guys, there's been about 20 million threads on this already. I hate to say it, but the subject has really been worn out. I don't want to have to close this thread, but if it continues on the current path I will.

Why don't you try something like: [math]f : [0,1] \to \R, \ f(x) = \begin{cases} 1 & x \in \Q\\ 0 & x \notin \Q \end{cases}[/math] That's rather a nasty little function.

Okay, I think that this has gone on long enough. Pretty much the last page of this has been throwing insults back and forth over and over again, and as such I'm going to close the thread. Any requests for re-opening the thread can be directed towards myself.

I should probably add that once you have proved your conjecture, it's a fairly simple affair to get a formula explicitly in terms of n, using the Binet formula for Fn, as mezarashi has given it.

Okay, so let's look at some numbers; F_n is the n'th fibonacci number, S_n is the sum of the first n numbers; i.e. [imath]S_n = \sum_{k=1}^{n} F_k[/imath]. n 1 2 3 4 5 6 7 8 9 10 F_n 1 1 2 3 5 8 13 21 34 55 S_n 1 2 4 7 12 20 33 54 ... Whilst I would quite like to give you the answer straight away, we do have a policy of not giving out explicit answers unless you show a significant amount of working. I will, however, say this: observe what happens when we add 1 to the [imath]S_n[/imath]'s: n 1 2 3 4 5 6 7 8 9 10 F_n 1 1 2 3 5 8 13 21 34 55 S_n+1 2 3 5 8 13 21 34 55 ... The way I've written it should give the obvious corellation between [imath]S_n + 1[/imath] and [imath]F_{n+2}[/imath]. From there, it's fairly trivial to prove using induction.

Perhaps writing down the Fibonacci numbers next to the sum would help. Just stare at it; after a while it should leap out.

I should think so. Even if you can't buy the actual spares themselves, take a look on eBay; a quick search for "xbox spares" brought up quite a few knackered up Xboxes that you can use for spare parts. I don't know the answer to this one. I would have thought so, but you're going to want to ghost the drive, since erasing it probably wouldn't be a good idea (it has the Xbox software on it, presumably). Easier just to go out and buy yourself a 20/40gb hard drive.

I also recommend X-Chat; if you want a Windows build, have a look at http://www.silverex.info/ for a free, non-shareware version.

The best advice I can give you is to draw it out and observe what integrals you need to consider. A plot is always useful in these cases.

Use ephPod. When I moved to university, I transferred all of my music over from my ancient iMac to a new PC. I got the iPod out, made sure it was sync'd with the iMac, plugged it into the PC and then booted up ephPod. Transferred ~10gb music over in about 15 minutes or so.

No, you can assume the answer is X(t)T(t), and then obtain 2 ODEs from this, allowing you to get solutions fairly easily.

This is just all rubbish.

Topologies are rather a different beast to anything you've touched there. Differentiation, integration and calculus etc is all very well and good, but you need to take it to the "next level", so to speak. Topological spaces attempt to basically extend the ideas of continuity, sequences and things like this to more abstract spaces than the reals. Along the way, you can touch on things like connected-ness, compactness, completeness and the like. If I were you, I would strongly recommend reading up on analysis of real-valued functions, and study a lot of things such as continuity, etc. You might also find it useful to concentrate on analysis of functions such as [imath]f:\R^n \to \R^m[/imath], since a lot of the topics have a certain amount of overlap. When you've done this, you can take a look at metric spaces, and then wean yourself onto topologies. It's by no means a simple option to take. Topologies are very abstract and can be quite hard to visualise. If you want some examples, I can give some

I don't think you're going to need to buy much; there's plenty out there in the way of free/shareware utilites to benchmark pretty much every application you need.

They already exist; they're called caddy drives, you can pull them out and put other ones in.

Moved to Homework Help.