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closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$ How do I create an invisible character? I cannot remember how to create an invisible character in LaTeX, i.e. I want to put a space that has the width of a particular character, say `M'. I know there is a command for this, and this is a really dumb question, but my Google-fu has failed me. sum of the residue at all poles of the rational function p/q is 0. We are given two polynomials p, q with deg(q)>1+deg(p). Show that the sum of the residue at all poles of the rational function p/q is 0.   How do I go about solving this? What is the analytic continuation of the Riemann Zeta Function Simulating a Brownian Excursion using a Brownian Bridge? As it is common with people from my country, I have an immense difficulty with prepositions in English, especially with the use of in and on.   When the preposition indicates the position of the object it is a bit easier to decide which one to use, but as it requires thinking from me, I still say things like "I put the bill in the fridge", "my pencil is on my bag", etc, even though if I think about it, I would know how to say it correctly.  Of course, even in those cases where the preposition indicates position the decision is not always clear, as is the case for example with "on the bus" (you are not on top of the bus, you are inside the bus) or "he is in bed" (you are not inside the bed, you are on top of your bed).  Other cases are even less clear, and I believe there is no real rule to decide what should be said; the person should just know it. Two examples are "in a bad mood", "you are on my mind".  So my first question is whether there is really no rule to help me. The second question refers to two of the cases where I still don't know whether to use in or on:   good luck on/in your exam in/on the list   The last one is especially important to me, as I have asked a number of native speakers, and each time I get a different answer. The only consensus seems to be the case where you say "on top of the list". Apart from that, some people will say that I should say "his name is in the list" whereas others think I should say "his name is on the list". And yeah, a couple of people did tell me that I can use either.  Can someone help me? Factor analysis and regression How to show that $\mathbb{Q}$ is not $G_\delta$ Unfortunately MyApp has stopped. How can I solve this? Try to do something vs. Try doing something Is there any differences between      Try to do   And     Try doing   Thank you in advence. Looking for the title of a gold heist movie involving the telekinetic son of an extraterrestrial/alien? Some 30 years back, I saw a film about the son of an extraterrestrial who gets involved in a gold heist.  The main character does not initially know that he is the son of an extraterrestrial and that has special telekinetic powers. The film opens, I think, with him being in some train yard, his foot getting stuck in a switch with a locomotive approaching. He stops it using his powers intuitively, possibly passing out (not realizing what he actually did). I think his mother subsequently reveals his heritage to him.  He somehow gets hired as a bodyguard for someone planning a gold heist. I think they know his abilities and use him to steal a million US dollars. Actually, that is just a distraction, covering that they steal 30 million dollars from the same location (through the air, not sure on that part).  The last part I remember is some underground tunnels where the thieves set up to melt the gold. The main character is locked in there.  Does anyone know the title of this movie? Searching for things like "sci-fi gold heist extraterrestrial etc." did not reveal anything to me. I also had a hard time picking proper tags (sorry). What system monitoring tools are available? I am looking for system monitoring tools which are GUI and CLI or web-based which include basic functions such as:   CPU Usage Ram Usage Swap Usage Disk Usage ( Space / I/O ) Heat Monitoring   I know there are many tools I can use, but I am looking for a single tool that has these basic functions. Preventing Brute Force Logins on Websites As a response to the recent  and , what is the best way to secure your website against brute force login attacks?  Jeff's post suggests putting in an increasing delay for each attempted login, and a suggestion in the comments is to add a captcha after the 2nd failed attempt.  Both these seem like good ideas, but how do you know what "attempt number" it is?  You can't rely on a session ID (because an attacker could change it each time) or an IP address (better, but vulnerable to botnets).  Simply logging it against the username could, using the delay method, lock out a legitimate user (or at least make the login process very slow for them).  Thoughts? Suggestions? How to understand intuitively the Stolz-Cesaro Theorem for sequences? I have to give a presentation on the theorem in Real Analysis with a fellow student. While I've looked over the  and verified that, yes, step B does indeed follow logically from step A, etc. and have internalized the proof to the extent that I can replicate it myself on paper, I still feel that I have made little progress as to why this theorem works the way it does, i.e. what is the intuition behind the theorem, such that it should make sense that it follows the way it does. Therefore I ask: what kind of intuition is there about this theorem? It would also be helpful to understand how the theorem can be used effectively in analysis.  I have seen it referred to as a sort of L'Hopital's rule for sequences, which certainly seems to make sense, but I similarly have little intuitive understanding of how that rule works, either.  I am asking this question not only for my personal understanding, but also for the sake of being able to present it in an illuminating manner, such that the rest of the class can also come away with the same sort of intuition of how the theorem works and how it is useful. Any help would be greatly appreciated.  EDIT: I should point out that the formulation of the theorem we are being tasked to prove is the following:  Let $\lbrace a_n \rbrace$, $\lbrace b_n \rbrace$ be sequences, ${b_n}$ strictly increasing and unbounded. Then if $\lim\limits_{n \to \infty} \frac {a_{n+1} - a_n}{b_{n+1} - b_n} = l$ for some $l \in \mathbb R$, then $\lim\limits_{n \to \infty} \frac{a_n}{b_n} = l$ also. Delete votes from users who later become moderators shouldn't prevent community undeletion According to Hubble's Law, how can the expansion of the Universe be accelerating? Scientists today think the expansion of the universe is accelerating.   According to Hubble's law, objects further away are moving faster than objects closer to us. The further away an object is, the further back in time we are seeing, so in the past objects moved faster (is this sentence correct?).  So because objects moved faster before than they do now, surely that's deceleration not acceleration?  my textbook says "if Scientists today think the rate of expansion of the Universe were decreasing then distant objects should appear different to Hubble's Law predictions: universe is accelerating. More distant objects would seem to be receding faster (since expansion was faster in the past)" Volumetric Windows 10 logo effect I'm trying to recreate the windows 10 background effect on a logo I've made in blender.  Half the logo has a glass like material, the other half has a steel like material. And I'm using cycles at the moment.  I've put various light sources behind the logo and tried a few variations of volumetric scatter in the world to get the god ray sort of feel coming off the logo, but it's just not looking anywhere near as effective as I'd like.  I know the win10 background was a real set and photographed, but has anyone come across a tutorial to do something similar in blender?  I'm very new to the tool, I'd appreciate any pointers in the right direction. Force JavaScript exception/error when reading an undefined object property? Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality.  While I don't fully understand it, Leggett's inequality takes this a step further and shows that we can't even have non-local realism theories.  Apparently there are some hidden variable theories that get around this by having measurements be contextual.  I've heard there are even inequalities telling us how much quantum mechanics does or doesn't require contextuality, but I had trouble finding information on this.  This is all confusing to me, and it would be helpful if someone could explain precisely (mathematically?) what is meant by: realism, locality (I assume I understand this one), and contextuality.  What combinations of realism, locality, and contextuality can we rule out using inequality theorems (assuming we have experimental data)? PHP function to build query string from array I'm looking for the name of the PHP function to build a query string from an array of key value pairs. Please note, I am looking for the built in PHP function to do this, not a homebrew one (that's all a google search seems to return). There is one, I just can't remember its name or find it on php.net. IIRC its name isn't that intuitive.