Evaluate $ \lim_{n\to\infty} \frac{(n!)^2}{(2n)!} $
Calculate $\lim_{n\rightarrow +\infty}\binom{2n} n$
Modular Arithmetic - Find the Square Root If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $ I am new to Ubuntu and Linux in general.  I created a dual boot OS on my laptop (Windows 10 and Ubuntu).    Typing: sudo apt-get install python3-tk (or even python-tk) didn't work. Trying to install the python3-dev or python-devel (no luck). Downloading Tcl and Tk to manually install.   In Windows 10 Bash Subsystem the Tk and Tcl are already included, so I thought Ubuntu already had it.  But, I want to use my Ubuntu desktop to develop Python GUI apps.   So, how can I install the Tcl/Tk to be use in Python 3.5 for GUI development?   I loaded Python 3.5.2 fine but need the GUI modules enabled.  The code to test that Tk is working is:      Type python3    Type:     import tkinter    tkinter._test()  Result: a GUI pop-up displaying This is a Tcl/Tk version.. On my MacBook Pro I have found that several applications seem to share the value for a find.  For example, I searched 'applestackexchange' in Safari's unified address bar, then I switch to Xcode and click into a Find field.  The first word of my search in Safari then appears there.  iTerm2 and Sublime Text 2 also seem to participate in this sharing.  Running latest Mountain Lion on  a 2012 MBP. Decorate Tables You have $r$ red, $g$ green and $b$ blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number $t$ of tables can be decorated if we know number of balloons of each color?  I know the answer will at least be $\min(r,g,b)$. Also we need to add tables with $2$ reds, $2$ blues or $2$ greens. I cannot think of the formula for it MathJax does not work on question title on Android app Although, the question is displayed correctly with MathJax when opened.   App Version: 1.0.85 Device Manufacturer: Spreadtrum Device Model: Celkon A35K   OS Version: 4.4.2 (eng.root.20140613.225402) Split a string with delimiters but keep the delimiters in the result in C# getting Checkpoint VPN SSL Network Extender working in the command line The official Checkpoint out command line tool from CheckPoint, for setting up a SSL Network Extender VPN is not longer working from the Linux command line. It is also no longer actively supported by CheckPoint.  However, there is a promising  project, that tries to replicate the Java applet for authentication, that talks with the snx command line utility, called snxconnect.   I was trying to put snxconnect text utility to work in Debian Buster, doing:  sudo pip install snxvpn   and  export PYTHONHTTPSVERIFY=0 snxconnect -H checkpoint.hostname -U USER    However, it was mostly dying either with an HTTP error of:   HTTP/1.1 301 Moved Permanently:   or:  Got HTTP response: HTTP/1.1 302 Found   or:  Unexpected response, try again.   What to do about it?  PS. The EndPoint Security VPN official client is working well both in a Mac High Sierra and Windows 10 Pro. How can I unlock a password locked rar file without knowing the password? I have .rar file that is password protected, but I accidentally have forgotten the password. The file extremely important to me.  How can I get my file back? In windows, there was many programs that could remove the password of such a file. Is there one for Ubuntu? Is there an algorithm to decide if a symlink loops? Unix systems usually just error out if they are confronted with a path that contains a symlink loop or just too many symlinks, because they have a limit to the number of symlinks they will traverse in one path lookup. But is there a way to actually decide if a given path resolves to something or contains a loop, even if it contains more links than a unix is willing to follow? Or is this a formally undecidable problem? And if it can be decided, can it be decided in a reasonable amount of time/memory (e.g. without having to visit all files on a filesystem)?  Some examples:  a/b/c/d where a/b is a symlink to ../e and e is a symlink to f and f is a symlink to a/b  a/b/c/d where a/b/c is a symlink to ../c  a/b/c/d where a/b/c is a symlink to ../c/d  a/b/c/d where a/b/c is a symlink to /a/b/e where a/b/e is a symlink to /a/b/f where a/b/f is a symlink to /a/b/g   Edit:  To clarify, I am not asking about finding loops in the file system, I am asking about a decision algorithm that decides of a given path whether it resolves to a definite file/directory or whether it does not resolve at all. For example in the following system, there is a loop, but the given path still resolves fine:  / -- a -- b where b is a symlink to /a   This directory tree clearly has a cycle, but the path a/b/b/b/b/b still resolves fine to /a. "Dear Sir or Madam" versus "To whom it may concern" When is it appropriate to use the terms Dear Sir or Madam and To whom it may concern?  The rules I was taught state that Dear Sir or Madam should be used when you're writing a letter to a person about something that person has direct involvement in (e.g. returning a defective product to a customer service department).  By the same rules, To whom it may concern would be used for situations in which the recipient is a third party to the topic of the letter (e.g. regarding a letter of reference or recommendation).  Was I taught correctly?  Is the rule actually something else?  Or is this one of those situations where many people have an opinion but there is no real rule? Looping through array and removing items, without breaking for loop What is Reflection in Java Can anyone explain? Can't run gparted in fresh system Trying to run gparted in fresh installed Ubuntu. System not found this program. When I try to install I have report that it is already installed. How to solve this problem?  g@g-Lenovo:~$ gparted The program 'gparted' is currently not installed. You can install it by typing: sudo apt install gparted g@g-Lenovo:~$ sudo aptitude install gparted [sudo] password for g:  gparted is already installed at the requested version (0.25.0-1) gparted is already installed at the requested version (0.25.0-1) No packages will be installed, upgraded, or removed. 0 packages upgraded, 0 newly installed, 0 to remove and 130 not upgraded. Need to get 0 B of archives. After unpacking 0 B will be used. Currency formatting in Python I am looking to format a number like 188518982.18 to £188,518,982.18 using Python.  How can I do this? What is the mass density distribution of an electron? Of course preventing them from getting stolen is the top priority, but invariably, someone is going to get jacked. What are some good practices to minimize the damage incurred when your PC is stolen?  Given most of our PCs contain our entire lives, its frightening to know that all this information can be in someone else's hands.   Some ideas i had (a bit paranoid, i admit).   keep encrypted backups.  Use truecrypt to have double encrypted (with strong password) volumes where you store your personal data. schedule Eraser to run every evening so that potential thieves couldn't undelete (and subsequently retrieve) sensitive data do all your banking in a virtual machine.  Keep the virtual machine volume encrypted, and on a portable usb drive that you carry with you / keep in a safe. have applications that phone home (or hit something to leave an IP trace) upon connection to the internet (can someone suggest a good solution for this?)   Does anyone have any other suggestions? How much Valyrian steel is there that is unused for link making and why aren't people making weapons out of it? I was reading  that stated Maesters can have Valyrian steel links:     Valyrian Steel links (for the study of Magic + the Occult) are exceedingly rare and held by less than one Maester in a hundred. Ironically, they aren't seen as especially prestigious but rather viewed with suspicion.   This made me wonder how much Valyrian steel there is lying around for Maesters to be adding them to their chains. It seems like such  resource like this would be used for crafting weapons not being kept as ingots ready for Maesters to make links.  Indeed the Wiki I linked above claims:     the amount of Valyrian steel in the world is finite and extremely rare   How much of his extremely rare resource is being kept in reserve for link making and why hasn't it been used for more useful stuff like making weapons? How do I find out which program and process ID accesses a given IP address in Windows? Is it possible to catch, which program is accessing a specific IP address?   I found my computer is flooding and wish to check addresses one by one.  May be it is possible to set up some audit for this? The Feeds bot’s translate command is no longer working for moderators