For the past 30 minutes I've tried to solve this identity but with no luck. I've tried with math induction,perturbation method and to write the sum and find some simetry but non of them worked. Could someone please help me? Thank you.  $\sum_{k=1}^{n}(-1)^{k+1}\frac{1}{k}\binom{n}{k} = 1+\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$
I've been trying to prove   $$\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$$  I've tried perturbation and inversion but still nothing. I've even tried expanding the sum to try and find some pattern that could relate this to the harmonic series but this just seems surreal. I can't find any logical reasoning behind this identity. I don't understand . Is there any proof that doesn't require the integral transform?
Why are these sites cloning my content, and how do I stop them? So I was searching for one of my own websites on Google: http://www.botlibre.com  and to my surprise found some clones of my website, like:  http://83waystowasteyourtime.adidas.com  and:  http:// mediaiq.astral.comm  My question are:   Why are they creating clones of my website?  Some kind of SEO scheme or what? What gain could they be getting? How do they have a URL at adidas.com and astral.comm?  I assume it's not Adidas steeling my content. How do I shutdown these sites and stop people from stealing my content? (on Tomcat) Strange grey bordering/outline in Illustrator I made a couple of vector shapes in AI and I get this strange thin border appearing around them. I can't get rid of it. Any suggestions?    Zoomed in: I recently got the book "selected problems in real analysis", and I'm stuck solving the very first problem  $(u_n)$ is a binary sequence iff it only contains $0$ and $1$ in the sequence  Let $A$ be the set of all binary sequences  I have to prove that $A$ and ${2}^{\mathbb{N}}$ have the same cardinality, that is to say there exists a 1-1 function from one set to another  I've thought about maybe considering integers as base-2 numbers  Thanks for your help I have an application that reads a CSV file with piles of data rows.  I give the user a summary of the number of rows based on types of data, but I want to make sure that I don't read in too many rows of data and cause OutOfMemoryErrors.  Each row translates into an object.  Is there an easy way to find out the size of that object programmatically?  Is there a reference that defines how large primitive types and object references are for a VM?  Right now, I have code that says read up to 32,000 rows, but I'd also like to have code that says read as many rows as possible until I've used 32MB of memory.  Maybe that is a different question, but I'd still like to know. Regular expression to match balanced parentheses I need a regular expression to select all the text between two outer brackets.  Example: some text(text here(possible text)text(possible text(more text)))end text  Result: (text here(possible text)text(possible text(more text))) I'm using Ubuntu 13.04 on a Lenovo X220.  Why do I have so many .Xauthority.* files in my home directory? I.e  .Xauthority .Xauthority.0JW6UW .Xauthority.2HWRVW .Xauthority.2TA6VW .Xauthority.49F8VW .Xauthority.4E27UW .Xauthority.7CLTVW .Xauthority.8JGGXW .Xauthority.96SAVW .Xauthority.AOUFVW .Xauthority.ASDOVW .Xauthority.CGVJXW .Xauthority.E0ZSVW .Xauthority.E5VZWW .Xauthority.FE64UW .Xauthority.FIHDWW .Xauthority.HL45VW .Xauthority.HYCCVW .Xauthority.ILUEWW .Xauthority.JXJHVW .Xauthority.K1QJXW .Xauthority.KXSOVW .Xauthority.LEKEVW .Xauthority.M48WVW .Xauthority.M6QTVW .Xauthority.MW6NWW .Xauthority.N57TWW .Xauthority.O5HAWW .Xauthority.OIC5VW .Xauthority.P2RPVW .Xauthority.Q0FRVW .Xauthority.QW01WW .Xauthority.RDW5WW .Xauthority.T0TLWW .Xauthority.TSO4WW .Xauthority.U6R9VW .Xauthority.V3KAWW .Xauthority.W8Z1WW .Xauthority.XDLGVW .Xauthority.XOOHWW.Xauthority.XUICVW  They are all zero bytes except the first, with timestamps all over the place.  What are these, and are they safe to delete? I just received a PhD invitation letter from a German University which mentions that my remuneration will be 2/3 of full TV-L 13 position. I do not know what a TV-L 13 position is (Google is of no help here), and didn't want to be rude, so I am asking here first. Is this a common position or specific to Germany? If anyone knows, currently how much remuneration corresponds to a TV-L position? Can't insert code in my beamer slide I want to put some PHP code in my slide with the package listings but I have this error message:  Argument of \frame has an extra }.&lt;inserted text&gt;\par }   My latex code :   \documentclass{beamer}  \usepackage[utf8]{inputenc}  \usepackage[T1]{fontenc} \usepackage[frenchb]{babel} \usepackage{setspace} \usepackage{color} \usepackage{listings}  \usetheme{CambridgeUS}   \begin{frame} \begin{large}     Contexte : \newline \pause \end{large}  \begin{itemize}     \item Avertir Drupal \end{itemize} \begin{lstlisting}  // Gestion du contexte ete2013 // Utilisation d'un nouveau template if (%variables['ctpage'] == "ete2013") {     variables['template_files']=array('page-ete'); } \end{lstlisting} \end{frame} Adding table of certain attributes to map layout? I am using ArcMap 10.2 and I'm looking for a way to add  a table containing certain fields from select elements from a featureclass to my map. Ive tried the add table option from the attribute table, but it doesn't quite give what I want (the table must be editable to look a certain way).   Are there any options out there for 10.2 like arcpy.mapping.tableview or will upgrading to 10.3 so I can get access to the "graphic table element" function be best? Taking screenshot of a specific area from the command line I've installed emacsformacosx on my OSX box.  I'd like to shove my macmini in a data center and run it headless.  I've gotten x-windows working.  If I run xeyes, it displays on my Windows 7 client.  Emacs works from the command line on the osx box.  However, if I start up emacs from the windows client, it pops it up on the server instead of the client.  What am I doing wrong? How much creative independence are the Show runners accorded in Game of Thrones? Since Season 3, we have been observing that the show was taking a different direction than the books. Many important characters never made it into the show, others who are still alive were killed off.   As we know the show is supposed to be based on the books, not to be direct adaption of the books from print to television media, there's bound to be a certain degree of creative independence accorded to them by the author of the series, George R.R. Martin.   The question is, how much independence do they have? Do they still have to take GRRM on board with whatever changes they might intend to make? By "they" I mean D&amp;D and the whole writers crew for the show. Given the number of significant changes they have made, I reckon the answer would be a lot. Has GRRM or HBO ever commented on that? So I'm in Linux and I want to have a program accept arguments when you execute it from the command line.  For example,   ./myprogram 42 -b -s  So then the program would store that number 42 as an int and execute certain parts of code depending on what arguments it gets like -b or -s. Learning Regular Expressions I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them? "You're too clever a man" JSON.parse: unexpected character I would like to work out the Fourier transform of the Gaussian function   $$f(x) = \exp \left(-n^2(x-m)^2 \right)$$  It seems likely that I will need to use differentiation and the shift rule at some point, but I can't seem to get the calculation to work. Does anyone have any advice?  By the way, I am using   $$\mbox{FT}(f)(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,\mathrm d x$$  as my definition of a Fourier transform. Many thanks. I'm trying to figure out how to use "not only... but also" properly. Basically, my goal is to combine two clauses by using "not only".  For negations, I've figured out two styles that both sound correct:   He knew that if he fractures his finger, not only would he not be able to compete in the water polo tournament, he would not be able to take the SAT on Monday, either. He knew that if he fractures his finger, neither would he be able to compete in the water polo tournament, nor would he be able to take the SAT on Monday.   However, I don't know how to form a sentence that does not include a negation while using "not only". Here are a few possibilities that I've considered:   Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was also given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was also given a full scholarship.   In those four possibilities, I'm varying the usage of "but" and "also" in the last clause.  What is the proper usage of "not only"? On duplicate questions, I often see different headings for the duplicate question list. These include:     Possible Duplicate:    [duplicate question list]   and      This question already has an answer here:    [duplicate question list]   and more recently,     This question is an exact duplicate of:    [duplicate question list]   What decides which heading is placed before the duplicate question list? Where is a good place to learn classical optics for high school competitions? I need to learn basic optics for a high school academic competition. Does anyone know any good places, preferably free and online, to learn the basics of optics, like lenses, angles of incidence, etc.? I can't seem to find an MIT OpenCourseWare course addressing the issue.