Is $a_n = \frac{1}{n}+\frac{1}{n+1}+...+\frac{1}{2n}$ convergent? If so find its limit.  Heres what ive tried:  $... &lt; \frac{1}{n}+\frac{1}{n+1}+...+\frac{1}{2n} &lt; \frac{n}{n} = 1$  What should I put on the left side of the inequality? I tried $\frac{n}{2n}$ but that tends to a half and I cant think of solving this in any other way except the squeeze rule.
What is the sum of the 'second half' of the harmonic series?  $$\lim_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} =~ ?$$  More precisely, what is the limit of the above sequence of partial sums?
What is the relation between normal extension and separable extension? What is the relation between normal extension and separable extension? Let F be the algebraic extension of K, if F is a separable extension of K,if and only if F is a normal extension of K? is this correct? Why can't I cd to a quoted tilde ('~')? Writing my first script so I'm sure this is a basic question, but can someone please explain to me why I can:  cd ~ cd bin cd ~/bin cd 'bin'   But not  cd '~' cd '~/bin'   I need to cd to a directory path with a space in one of the directory names, so I need the quotes (it's Windows Program Files under wine). I can get around it with two cd commands, but why can't I put ~ in quotes?  If I type cd '~' (or cd "~") I get:  bash: cd: ~: No such file or directory DNS, multiple nameservers and geolocation? Currently, when a DNS client makes a request for a DNS record (say, www.example.com., it needs to traverse the DNS tree. It asks the root servers for the location of com., which it then asks for the location of example.com., which it then asks for the location of www.example.com.. Thankfully, much of this is cached.  If example.com. has multiple, geographically diverse NS records listed, my understanding is that these are listed in random order to avoid all queries going to the first (or last) NS record listed.  This would appear to imply that a DNS resolver in Australia could choose a NS record for a nameserver that's located far away, perhaps in Europe, when there may be another authoritative nameserver that is much closer.  So, my question is: Is there any provision within the DNS spec to allow DNS resolvers to select an authoritative nameserver that's local to them? The only way I can see to achieve this is to have the NS records behind an anycast address and do local resolution that way. Would this work? Is there any other option? What are the differences between a pointer variable and a reference variable in C++? I have a directory on my Windows 7 machine that has hundreds if not thousands of sub-directories.  Some of them have files, some do not.  I want to delete all the empty directories.  Looking at the del and rmdir DOS command, it does not look like you can recursively do this without deleting all the files.  Is there a way to do this from the command line? Parsing XML, JSON, and newer data file formats in UNIX using command line utilities The Unix environment has some excellent tools for parsing text in various forms. However, of late, the data is not in the traditional (historical) formats (CSV, TSV, record-based or some other delimiter-based) it used to be before. Data these days is exchanged in structured formats like XML/JSON.  I know there are some good tools like sed, awk and Perl which can chew down nearly any form of data out there. However, to work with this sort of structured data, often one has to write a complete program, and, given the little time available to extract information, one has to sit down and figure out the whole logic of what one wants to query and put it down programmatically. Sometimes this is not OK – basically because the information extracted from those files acts as inputs for further work; also because of the time it takes to search for the appropriate solution and code it up. A command line tool is needed with sufficient switches to find, query and dump data.  I'm looking for tools that take a XML/JSON or other forms of structured data and dump it into other formats like csv, etc., so that from there one could use other commands to get any information out of it.  Are there any command line utilities you know of which do this kind of a job? Are there already awk/Perl scripts available to this? Infix to postfix not working as expected Which equals operator (== vs ===) should be used in JavaScript comparisons? Like the ModelBuilder of ArcGIS Desktop to run simultaneous geoprocessing tools, is there any model builder available in QGIS? Regular Expression to split on spaces unless in quotes I would like to use the .Net Regex.Split method to split this input string into an array. It must split on whitespace unless it is enclosed in a quote.  Input:  Here is "my string"&nbsp;&nbsp;&nbsp;&nbsp;it has "six&nbsp;&nbsp;matches"  Expected output:   Here is my string it has six&nbsp;&nbsp;matches   What pattern do I need? Also do I need to specify any RegexOptions? Is the .minecraft folder hidden on a Mac? Changing the value of an element in a list of structs I have a list of structs and I want to change one element. For example :  MyList.Add(new MyStruct("john"); MyList.Add(new MyStruct("peter");   Now I want to change one element:  MyList[1].Name = "bob"   However, whenever I try and do this I get the following error:     Cannot modify the return value of   System.Collections.Generic.List.this[int]‘ because it is not   a variable   If I use a list of classes, the problem doesn't occur.  I guess the answer has to do with structs being a value type.  So, if I have a list of structs should I treat them as read-only? If I need to change elements in a list then I should use classes and not structs? Real Size Image Printing Best book of topology for beginner? I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one.. Ring homomorphism and characteristic What is this noisy shadow overlay that stays with the camera? Get Age of a person in MySQL How do I get a list of obsolete packages? I'm trying to figure out a way to get a list of the packages that are no longer available in the repositories that I have enabled. This workstation has been through quite a few versions of Ubuntu and has had many 3rd party repositories added and removed. I'd like to get a list of software that I have from these removed repositories, so I can clean it up or add back the appropriate repositories. SCP fails without error How can I set the maximum draw type for multiple objects?