$$ \sum_{b=1}^{n} \left\lfloor\frac{n}{b} \right\rfloor $$   I can't figure out how to convert this into a closed form.  Edit: I often come across summations I'm unable to solve. Is there some resource from which I can learn/practice solving complex summations. I hate asking numerous small questions of the same type repeatedly so if you could give some advice, I would be really grateful.
$$ \sum_{i=1}^N\left\lfloor\frac{N}{i}\right\rfloor $$ Is there a closed form expression to the above sum? (Mathematica doesn't give me anything)
Series rearrangement and Riemann's theorem I think understand that when I have a conditionally convergent series, it consists of series of positive and negative values which are divergent and thus one can find such permutation of indices $\phi : \mathbb{N}\rightarrow\mathbb{N}$ so the rearranged series sums up to an arbitrary value, diverges or oscillates.   This is how I understand what Riemann's rearrangement theorem says, but how do I use it practically? For example, when I have the conditionally convergent series:  $$\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n}}$$  and I want to rearrange it to be divergent or to sum up to certain value M? How do I define such bijections $\phi$ ?  I appreciate all help. Parsing an Int from a string in javascript In javascript, what is the best way to parse an INT from a string which starts with a letter (such as "test[123]")?  I need something that will work for the example below.  My JS:  $(document).ready(function() {      $(':input').change( function() {         id = parseInt($(this).attr("id"));  //fails for the data below         alert(id);     }); }   My generated HTML:  &lt;select id="attribute[123]"&gt; &lt;!-- various options --&gt; &lt;/select&gt; &lt;select id="attribute[456]"&gt; &lt;!-- various options --&gt; &lt;/select&gt;   Thank you! dual boot missing files on ntfs I have 3 partitions: one for Windows 7 (ntfs), one for Ubuntu (ext4) and one just for data (ntfs so both operating systems can see them).  My problem is that I had stored some files on the data partition using Ubuntu and when I booted Windows 7 all that data was gone! After that I couldn't find the files even when using Ubuntu.  My files were simply GONE :(  Is there something I can do in Ubuntu or is it just windows problem? If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$ Passing parameters to a document I compile most of my documents via Makefiles which take care of the bibliography, indexes, etc. Often I'd like to compile different versions from the same TeX file changing only small things (e.g. a beamer presentation plus a version with the handout option).  Is there any standard mechanism for passing parameters to the TeX file so that I can just type make handout to get the handout version in the above example? Is it possible to start windows with NUM Lock on? A password is always combination of characters &amp; numbers. I am so much used to num pad that every time windows start I end up entering wrong password just because NUM lock isn't ON by default. Since it's network login, it takes a bit long time to reset &amp; prompt for right password. Is there a way to enable NUM Lock on when Windows loads? This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y? For each of the following, give an example of a sequence of functions $f_n$ that converges to f  A. uniformly but not in the mean square sense.  B. in the mean square sense but pointwise nowhere.  I know that for part A the domain of the function cannot be bounded but other then that I'm not sure how to go about the problem Comparing two logit or probit curves using a single parameter I've conducted a psychological experiment on the same subject, under two different condition. For each condition I've collected the number of correct and wrong answer for each stimulus (number of trials per stimulus = 10; number of stimulus = 15). From the data collected I fitted a psychometric curve (probit or logit curve), and now I want to compare the results.  Consider subject 1: His answers are collected in the following matrices  **COND_1**     correct cnt   Y  N   1   0 10   2   0 10   3   0 10   4   0 10   5   0 10   6   0 10   7   1  9   8   4  6   9   5  5   10  7  3   11  8  2   12  7  3   13 10  0   14 10  0   15 10  0  **COND_2**     correct cnt   Y  N   1   0 10   2   2  8   3   2  8   4   3  7   5   2  8   6   4  6   7   8  2   8  10  0   9   8  2   10 10  0   11  9  1   12 10  0   13 10  0   14 10  0   15 10  0  COND_1.1 &lt;- matrix(c(0, 2, 2, 3, 2, 4, 8, 10, 8, 10, 9, 10, 10, 10, 10, 10, 8, 8, 7, 8, 6, 2, 0, 2, 0, 1, 0, 0, 0, 0), byrow=F, ncol=2)  COND_1.2 &lt;- matrix(c(0, 0, 0, 0, 0, 0, 1, 4, 5, 7, 8, 7, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 6, 5, 3, 2, 3, 0, 0, 0), byrow=F, ncol=2)  cnt &lt;- seq(from=0, to=1.4, by=0.1)  ddprob.1.1 &lt;- glm(COND_1.1 ~ cnt, family = binomial(link = "probit"))  ddprob.2.1 &lt;- glm(COND_2.1 ~ cnt, family = binomial(link = "probit"))     Observing the plot, you can surely say that performance under condition 2 is better then the performance under condition 1. In fact if you compute some parameters like AUC, p25, p50, p75 (the value of the stimulus at which the number of correct answers are 25%, 50% and 75% each) [threshold parameters], you'll see that:  COND_1      COND_2 AUC    &lt;    AUC p25    &gt;    p25 p50    &gt;    p50 p75    &gt;    p75     Now consider subject 2:  COND_1     correct cnt   Y  N   1   0 10   2   0 10   3   0 10   4   0 10   5   3  7   6   3  7   7   4  6   8   5  5   9   9  1   10  9  1   11 10  0   12 10  0   13 10  0   14 10  0   15 10  0  COND_2     correct cnt   Y  N   1   0 10   2   1  9   3   0 10   4   4  6   5   2  8   6   6  4   7   4  6   8   7  3   9   4  6   10  7  3   11  7  3   12 10  0   13  9  1   14 10  0   15 10  0   COND_1.2 &lt;- matrix(c(0, 0, 0, 0, 3, 3, 4, 5, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 7, 6, 5, 1, 1, 0, 0, 0, 0, 0), byrow=F, ncol=2) COND_2.2 &lt;- matrix(c(0, 1, 0, 4, 2, 6, 4, 7, 4, 7, 7, 10, 9, 10, 10, 10, 9, 10, 6, 8, 4, 6, 3, 6, 3, 3, 0, 1, 0, 0), byrow=F, ncol=2) cnt &lt;- seq(from=0, to=1.4, by=0.1)  ddprob.1.1 &lt;- glm(COND_1.2 ~ cnt, family = binomial(link = "probit")) ddprob.2.1 &lt;- glm(COND_2.2 ~ cnt, family = binomial(link = "probit"))   The plotted curves are shown in the image below.    Can you say what performance is better? Under condition 1 or under condition 2? Extrapolating AUC, p25, p50, p75, you have:  COND_1      COND_2 AUC     &gt;   AUC p25     &gt;   p25 p50     =   p50 p75     &lt;   p75   So my question is: Is there a method to say that a generic curve (logit, probit or whatelse) is HIGHER then another? Is there a method to compare (a single number of "performance") that describe the differences of the two curves? My example shows that AUC, p25, p50, p75 are not good parameters. I'd like to compute a single numeric parameter for each curves, to make a simple t-paired test, extrapolated from the distribution seen. Notify instantly when a currently viewed post is deleted At the moment SE shows us current voting results, a notification for new answers and comments, etc., instantly. However, it doesn't show us when a post is deleted.  Please notify us also when a post is deleted. Then I don't have to type a (long) comment, only to notice the post got deleted in the meantime. How do I send SMS from PC through Android Phone or to Android Phone? I'm looking for an app that will let me type text messages on my PC and send the SMSs directly from the PC through my phone, or save the messages to the phone for later use.  I'm basically looking at something like Nokia PC Suite's equivalent.  EDIT:  Google Voice is only for US, doesn't work in India at least, and also defeats the purpose (it will go through the internet, why, when it's possible through the usb cable/modem/wifi). DesktopSMS is a good program, but kept crashing, for some reason. PDANet worked for me. But I liked the tiny . It's weird, and I had to change the bluecove library jar file for Windows 7 x64, but it's compact (a concern for me). While CtrlX works fine in vim under windows, CtrlA selects all (duh).  Is there a way to increment a number with a keystroke under windows? How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$? I predicted the formula by finding total number of non-isomorphic labelled trees of order 1 is 1 , order 2 is 1,order 3 is 3,order 4 is 16,order 5 is 125.But how do i prove it ? I am beginner in graph theory so i will be very thankful if i get some simple approach to solve the problem(Not by using some difficult theorems). Closed form for an infinite product The following fascinating formula appears in the paper  by M.Chamberland and A.Straub (see page 9): $$\prod_{n=2}^\infty\left(1-\frac{1}{n(n-1)}\right)=-\frac1\pi\cos\left(\frac{\sqrt5}{2}\pi\right).$$ Unfortunately, it's given without any reference or explanation. Could anyone give one? Hello I'm writing a beamer presentation and I would like to change the colour of the text in the theorem block from one place and it will affect my whole presentation.  Is this possible?  My example:  \documentclass{beamer}   \usetheme{Madrid}   \usecolortheme[RGB={201,20,35}]{structure}   \setbeamercolor{background canvas}{bg=black}  \setbeamercolor{normal text}{fg=white}   \setbeamercolor{theorem text}{fg=black}    %\useoutertheme{shadow}  \useinnertheme{rounded}   \usepackage[utf8]{inputenc}  \usepackage{default}   \begin{document}   \begin{frame}{Primul Slide}   Bla bla bla    Bla bla bla   \begin{theorem}  This is a theorem it is very important!!  \end{theorem}   \end{frame}   \end{document} How can we discipline a strong-willed, misbehaving 5 year-old? My 5 year old son receives and fears punishment but repeatedly exhibits the same unacceptable behaviors.  He's always been strong-willed, and is usually the kind to view a statement like "Don't do that" as an open invitation to do it.  We've tried redirection or distraction tactics, but he is still so narrowly focused on doing the original behavior.  Even worse, he will typically do the prohibited behavior and flagrantly tell us or show us that he's done it.  Repeatedly, even after punishment.  (He's in time out right now for this very thing).  He's consistently punished, yet he continues down the same self-destructive path each time.  When he is punished, we explain what he did wrong, why he's being punished, and why he shouldn't do what he was told not to do.  Sometimes he'll even tell us first why he's in trouble, so it makes me wonder if he's acting out for the inevitable negative attention he gets.  I think he gets plenty of love and positive attention- he's an only child and stays with a relative during the day.  We're trying to give him a good, fun childhood, but we need to figure out how to effectively discipline him.    His repeated misbehavior includes:   Yelling at the top of his lungs in public (stores, friends' houses, etc) Running away from us (at parks, stores, parking lots, etc) Talking back and disrespecting authority figures Hurting animals even after we explain why it's wrong Repetitive nuisance behaviors (repeating himself, banging his fists, kicking walls, intentionally crumbling food on floors, etc) Repeatedly asking us why he can't do something even after it's been explained to him Basically, most bad behaviors that young children may do, but repeated over and over again, even after discipline   He gets a warning to stop the behavior, then depending on the severity of what he's done (and where we are), he'll either go to time out or lose a privilege (such as taking away a favorite movie or missing out on an activity).  Going to time outs and losing privileges really upset him, but still do not ultimately deter him from the bad behavior.  It's like he can't help himself.  My spouse and I are getting worn down.  We try to model good behavior and encourage him to be well-mannered and respectful.  This behavior mortifies us.  It seems we can't even enjoy life as a family because our son is so disruptive and unresponsive.  Most public outings have to be cut short or eliminated because he consistently misbehaves and doesn't respond to our discipline.  After he's misbehaved, when we try to have heart-to-heart talks with him about his behavior and why we expect him to mind us, he usually has a little trouble expressing himself, and a lot of times we get the same nonsensical responses from him (Us: Why did you do [bad behavior]?  Him: Because I didn't want to).  He also doesn't like to make eye contact.  We don't usually feel like we've gotten through to him.  Is there another discipline tactic we could try?  Or does it sound like we need to see a professional at this point?  We're at a loss, and don't want things to spiral further out of control as he gets older (and even begins school).  We just want him to understand that his behavior isn't always acceptable.  Thanks for reading.  Update (from comments below): My spouse and I disagree on spanking, as we had different experiences with it. He feels it's necessary sometimes. Since our son failed to improve after time outs and taking away items/privileges, I grew to agree with him and we used it for select bad behaviors. It didn't work any better. However, when he was spanked, he was always told why. I didn't mention that we have used it because I was afraid it would distract from the original question, but since it has already come up [in comments], yes, it has been explored, but with no better results than our other tactics. How to find a generator of a cyclic group? Do I need to re-check my bags when flying into the US on a transit through Newark Airport? Travveling with SAS 907 from Oslo, Norway to Newark Terminal B. Transfer to Terminal C and further with United 239 to Nashville. Do I have to pick up the luggage at terminal B and bring it to terminal C? How to fix slow wireless on machines with Intel wireless cards? I have looked through all the previous questions but turning power management off for the Wi-Fi card didn't work. This problem seems to be with the Lenovo Thinkpads. I switched to Ubuntu 11.10 from Windows 7 3 days ago so I'm new to the operating system. Where, how and when I can acquire HM's?