Sum of $50$ terms of $\cot^{-1}3+\cot^{-1}7+\cot^{-1}13+\cot^{-1}21+.....$
Explicitly finding the sum of $\arctan(1/(n^2+n+1))$
Can't run a shell script So I have this script:  #!/bin/bash # Flips the screen (hopefully)  syntax_error=0 orientation=0  current_orientation="$(xrandr -q --verbose | grep 'connected' | egrep -o  '\) (normal|left|inverted|right) \(' | egrep -o '(normal|left|inverted|right)')" case $current_orientation in         normal)                 current_orientation=0         ;;         left)                 current_orientation=1         ;;         inverted)                 current_orientation=2         ;;         right)                 current_orientation=3         ;; esac  if [ $current_orientation -eq 0 ]; then         orientation=2 fi  if [ $current_orientation -eq 2 ]; then         orientation=0 fi method=evdev  # LENOVO S10-3t CHANGE ==&gt; Hard Coded my device number to 11!!!!!!!!  device=11  swap=0 invert_x=0 invert_y=0 real_topx=0 real_topy=0 real_bottomx=4020 real_bottomy=4020  case $orientation in         0)                 swap=0                 invert_x=0                 invert_y=0                 topx=$real_topx                 topy=$real_topy                 bottomx=$real_bottomx                 bottomy=$real_bottomy         ;;         1)                 swap=1                 invert_x=1                 invert_y=0                 topx=$real_topx                 topy=$real_topy                 bottomx=$real_bottomy                 bottomy=$real_bottomx         ;;         2 )                 swap=0                 invert_x=1                 invert_y=1                 topx=$real_topx                 topy=$real_topy                 bottomx=$real_bottomx                 bottomy=$real_bottomy         ;;         3 )                 swap=1                 invert_x=0                 invert_y=1                 topx=$real_topx                 topy=$real_topy                 bottomx=$real_bottomy                 bottomy=$real_bottomx         ;; esac  if [ $method = "evdev" ]; then         xinput set-prop "$device" "Evdev Axes Swap" $swap         xinput set-prop "$device" "Evdev Axes Swap" $swap         xinput set-prop "$device" "Evdev Axis Inversion" $invert_x $invert_y         xinput set-prop "$device" "Evdev Axis Calibration" $topx $bottomx $topy $bottomy         if [ $orientation = 2 ]; then                            xrandr -o inverted         fi         if [ $orientation = 0 ]; then                 xrandr -o normal         fi fi  #   It's for flipping screen in my Lenovo S10-3t. I copied it from the netbook's wiki page, and added the #!/bin/bash at the top. The filename is flipscreen.sh. How can I make it work? I recently purged Libreoffice because it was buggy.  I then reinstalled the latest version from apt and now it's missing the symbols above the equation editor.  Here is the current Texmaths equation editor:   There used to be shortcuts for latex including frac{}{} and various set theory operations, as well as the binomial distribution on the top of the window.  What happened to them and how do I get them back? I just figured that they were in some package and installed all packages useing sudo apt install libreoffice*, but this didn't help after I refreshed the program.  EDIT 0: I'm using Kubuntu 19.04  sarah@LesserArk:~$ sudo apt-cache policy libreoffice-texmaths libreoffice-writer texlive libreoffice-texmaths:   Installed: 0.43-2   Candidate: 0.43-2   Version table:  *** 0.43-2 500         500 http://us.archive.ubuntu.com/ubuntu disco/universe amd64 Packages         500 http://us.archive.ubuntu.com/ubuntu disco/universe i386 Packages         100 /var/lib/dpkg/status libreoffice-writer:   Installed: 1:6.2.2-0ubuntu2   Candidate: 1:6.2.2-0ubuntu2   Version table:  *** 1:6.2.2-0ubuntu2 500         500 http://us.archive.ubuntu.com/ubuntu disco/main amd64 Packages         100 /var/lib/dpkg/status texlive:   Installed: 2018.20190227-1   Candidate: 2018.20190227-1   Version table:  *** 2018.20190227-1 500         500 http://us.archive.ubuntu.com/ubuntu disco/universe amd64 Packages         500 http://us.archive.ubuntu.com/ubuntu disco/universe i386 Packages         100 /var/lib/dpkg/status Help finding the limit of $\lim_{n \to \infty}\prod_{k=1}^{n}\left(1+\frac{1}{n}f\left(\frac{k}{n}\right)\right)$. A word used to describe someone who loves to be photographed Overview:  Lots of games with RPG-like statistics allow for character "buffs", ranging from simple "Deal 25% extra damage" to more complicated things like "Deal 15 damage back to attackers when hit."  The specifics of each type of buff aren't really relevant.  I'm looking for a (presumably object-oriented) way to handle arbitrary buffs.  Details:  In my particular case, I have multiple characters in a turn-based battle environment, so I envisioned buffs being tied to events like "OnTurnStart", "OnReceiveDamage", etc.  Perhaps each buff is a subclass of a main Buff abstract class, where only the relevant events are overloaded.  Then each character could have a vector of buffs currently applied.  Does this solution make sense?  I can certainly see dozens of event types being necessary, it feels like making a new subclass for each buff is overkill, and it doesn't seem to allow for any buff "interactions".  That is, if I wanted to implement a cap on damage boosts so that even if you had 10 different buffs which all give 25% extra damage, you only do 100% extra instead of 250% extra.  And there's more complicated situations that ideally I could control.  I'm sure everyone can come up with examples of how more sophisticated buffs can potentially interact with each other in a way that as a game developer I may not want.  As a relatively inexperienced C++ programmer (I generally have used C in embedded systems), I feel like my solution is simplistic and probably doesn't take full advantage of the object-oriented language.  Thoughts?  Has anyone here designed a fairly robust buff system before?  Edit: Regarding Answer(s):  I selected an answer primarily based on good detail and a solid answer to the question I asked, but reading the responses gave me some more insight.  Perhaps unsurprisingly, the different systems or tweaked systems seem to apply better to certain situations.  What system works best for my game will depend on the types, variance, and number of buffs I intend to be able to apply.  For a game like Diablo 3 (mentioned below), where nearly any bit of equipment can change a buff's strength, the buffs are just character stats system seems like a good idea whenever possible.  For the turn-based situation I'm in, the event-based approach may be more suitable.  In any case, I'm still hoping someone comes along with a fancy "OO" magic bullet which will allow for me to apply a +2 move distance per turn buff, a deal 50% of damage taken back to the attacker buff, and a automatically teleport to a nearby tile when attacked from 3 or more tiles away buff in a single system without turning a +5 strength buff into its own subclass.  I think the closest thing is the answer I marked, but the floor is still open.  Thanks to everyone for the input. How can I restrict the Normal user to run the only limited set of commands in RHEL? I want to make a power DC supply with voltage rating 0-200V. I want it to be a variable power supply with voltage from 1V to 200v. What should be my approach? Why does pdfTeX hang on this file? How to know current name of the database in Django? Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$ I noticed that I have three warnings when I submitted my Sitemap. They all say this:      When we tested a sample of URLs from your Sitemap, we found that some   URLs redirect to other locations. We recommend that your Sitemap   contain URLs that point to the final destination (the redirect target)   instead of redirecting to another URL.   I'd like to try and resolve this issues but I'm not sure what to do.  Sitemap url for reference: I don't know anything about Star Trek except for the fact that it's about spaceships.  In  the person only wanted to watch the TV series. I want to watch every movie and TV series there is about Star Trek but I don't know where to start. I found this page on  which is about a time line. Do I need to watch it in this order? Are the movies and TV series related? How to clone/copy all file/directory attributes onto different file/directory? I want to copy the attributes (ownership, group, ACL, extended attributes, etc.) of one directory to another but not the directory contents itself.  This does not work:  cp -v --attributes-only A B cp: omitting directory `A'              Note: It does not have to be cp. Is a continuous function on a bounded set bounded itself? If $f\colon A\to\mathbb R$ is continuous and $A$ is a bounded set, does it necessarily follow that $f$ is bounded? How does conservation work in wormholes? My questions might seem naive as I haven't plunged into the mathematical descriptions, but wormholes are interesting even if I don't actually know them :)  First of all, is wormhole making two possible paths betwwen points (like the tunnel in most visualisations) or is it just making two points beside each other like in the game Portal? Of course, second case can be bent into a tunnel, but there would be nothing special about tunnel part and no preferred way to divide into "normal" and "tunnel" part of spacetime.  My main questions are these:   Is momentum conserved? Is kinetic energy conserved? How does potential energy work?   To elaborate... In the game Portal you can fall into floor and fly out of the wall or floor elsewhere with the same speed, but another direction (normal to the portal). So momentum is not conserved, but kinetic energy is. Is that how it would actually work? Where does the momentum go then?  And does it really allow you to increase your potential energy while retaining kinetic? It would seem fair to take away some kinetic energy if you are put in a region where you have more potential energy.  Either way is the change in energy non-continuous like in the game and discussion that's linked below? Or are there just more than one way to move through but the change in potential energy is smooth in any of those? That would mean more potential equilibrium points though...  Similar questions has been discussed , is it correct about how the falling guys gets a lot of energy (in form of a potential one) by draining it from the mouths? What is a magic number, and why is it bad? What is a magic number?  Why should it be avoided?  Are there cases where it's appropriate? problems with ellipse TikZ I'm working on a mac, I use the package TikZ and it works. But I have problems when I want use ellipse or diamond ex :  \documentclass{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[ellipse] {Ellipse}; \end{tikzpicture} \end{document}   If somebody could help me thank you ! Can we have a moderator only "flag for community team/developer attention" link on posts? There are times when moderators come across things that only Stack Exchange employees can deal with. These include things like deleting sensitive information permanently from posts disassociating users from posts that require direct database access.  (The previous use case is now possible for moderators to do directly the moderator redaction tool)  Currently the workflow is:   See the post (either in normal site usage or via a flag) Go to chat Ping one of the community team (if they are around) Explain the problem   A far better workflow for the moderator would be to simply able to flag the post so it then appeared in an "employee only" queue somewhere. This could either be a page on the main Stack Exchange site or (better still) their inbox.  (OK I admit I hadn't fully thought this last bit out.)  This could either be a moderator "flag to devs" link on the post or a new option on the existing flag dialog (probably the better solution).  Now that moderators can't merge we have a fairly common situation where this would be very useful. A new users posts an answer (or question on sites that don't require registration) then loses their cookies and ends up creating another unregistered account (or two). Eventually the might even create a registered account. It used to be easy to merge the unregistered accounts into the registered ones, but now we either have to badger the OP to use the "merge accounts" form or ping the team somehow.  Having the "flag for team" option would be very useful in this scenario. Can I prevent others from editing my question? edited my question,  where I specifically said that our software sending back stacktrace to one of our servers was a user-known public feature.  He then modified the title of my post, along with the entire content, making it sound like I snuck in the feature and that our application was phoning home without our users knowing.    I specifically wrote in the original post that the feature was not sneaky. He completely changed the meaning of my post. I find this to be rather unacceptable.  A few questions:   Is it possible to prevent editing of my posts? How can I retaliate? Can I file a complaint?   Can people with  do anything they want on Stack Overflow? A borderline between on-topic questions and questions about library recommendation? I have a consideration about new off-topic close reason:     Questions asking us to recommend a tool, library or favorite off-site   resource are off-topic for Stack Overflow as they tend to attract   opinionated answers and spam. Instead, describe the problem and what   has been done so far to solve it.   For example take that question:   It has a close vote with the reason above. But if it would be formed     How to zoom image in an absolute position div to the side?   The answer would be probably also a jQuery plugin or javascript library, but it would follow the patter of most questions about jQuery.  Take that question:   This is the good question about real-life problem. The answer is to use a maven plugin. It is correct, there's no need to reinvent the wheel or rediscover the America.   But  I'm afraid the off-topic text could be misleading and could be misused to close such a questions as that about maven simply because a tool, library or plugin is the answer.   Is it a new guideline that the questions such as cited above should be banned, no matter how they are formed (this would make most how-to-do-in-maven/jquery) questions illegal? Or the close reason should be changed to make more clear what the guidelines are (it's not clear to me now)?