Sum of a series using squeeze theorem
Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$
In the sentence: "Drinking and driving IS dangerous", why does the verb "to be" need to be singular? In the sentence: "Drinking and driving is dangerous". Drinking and driving are both subjects and the word dangerous is the object (I think) but why do I have to use the verb to be in singular? How do I remove the OneDrive folder from my File Explorer folder tree in Windows 10? I don't use or want to use OneDrive, but after upgrading to Windows 10 it's been installed automatically and added to the sidebar of every explorer window:    I can't seem to figure out how to get rid of it. I can't uninstall it like a normal app, and I can't seem to unpin it in Explorer's options.  I tried following  to getting rid of it, but that seems to only remove stored OneDrive files.  I've also tried following another  and , but I can't seem to edit group policies on my computer (maybe because I upgraded from Win7 Home Premium?).  All I would really like is to be able to remove the OneDrive shortcut from my explorer sidebar, though being able to uninstall OneDrive would be a bonus.  I'm not sure what I should try now. Is there a way to remove OneDrive from Windows 10? White stains and stainless steel cookware I know this question has been asked before in some form or another, but I can't seem to find a definitive answer. I've looked on SA, chowhound, martha stewart, about.com, etc., and answers seem to vary. Answers that I've seen vary from using vinegar to washing using special stainless steel soaps (which I'm not very keen on using) to only using soft sponges and hot water.   The one thing I always do is wash my stainless steel with warm soapy water and a soft sponge. If there's burned food stuck on the cookware, I scrape it off with a wood pot scraper (lightly, of course). And I always dry with a soft cloth immediately after washing. Yet I still get stains!  I'd like to get a general consensus on how to prevent those white and rainbow colored stains as well as minimizing corrosion. Strange artifacts along window borders after waking computer from sleep mode Prove $|\arctan x - \arctan y|\leq |x-y|$ Basically, I want to turn a continuous "1" into a short "1" pulse then "0". I'm new to logic gates, apologies if it's too obvious. How to prove $\sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6$? I'd like to find out why  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6 \end{align}  I tried to rewrite it into a geometric series  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = \sum_{n=0}^{\infty} \Big(\frac{1}{2}\Big)^nn^2 \end{align}  But I don't know what to do with the $n^2$. Is it legal to run windows on a mac? I understand that it is Illegal to run OSx on a windows machine or PC for that matter, but is it illegal to do the reverse? Why or why not? Count the number of fish caught in total if we are given the number of fishermen who caught at least $n$ fish. Some fishermen caught some fish. No one caught more than 20 fish. $a_i$ is the number of fishermen who caught at least $i$ fish. How many fish were caught?   So my guess is that the number of fish caught has to be $$ a_1+a_2+\ldots + a_{20}$$  I reason that if a fisher man caught $n$ fish then he will appear in the tally $n$ times.   Is this logic correct? Divisibility Proof with Induction - Stuck on Induction Step I'm working on a problem that's given me the run around for about a weekend. The statement:  For all $m$ greater than or equal to $2$ and for all $n$ greater than or equal to $0$, $m - 1$ divides $m^n - 1$.  Using induction over $n$, the base step comes easy since $m^n - 1$ is $0$ when $n = 0$.  My induction hypothesis is letting $k \geq 0$ and assuming that $m - 1$ divides $m^k - 1$. In order to show that $m - 1$ divides $m^{k+1} - 1$, I obviously need to use the induction hypothesis. However, no matter where I try to use the fact that $m^k - 1 = (m-1)a$ for some $a$ in the integers, the expression $m^{k+1} - 1$ always becomes more difficult to get to $m^{k+1} - 1$ being equal to $(m-1)b$ for some $b$ in the integers.   In other words, I can't figure out any actually helpful way to apply the induction hypothesis with the goal of proving the next step.  Any help would be appreciated! Is there a place to dispute duplicate markings? How do I deal with a bored or distracted player bringing down the group? My group have been playing various D&amp;D style games for a few years,  I have one player however that often will drift off and start playing on his phone  and several times has actually fallen asleep (with his character having to be "nudged" along by his fellow players).  He insists he's "just tired" and "isn't bored" — and besides, he keeps insisting we all get together for D&amp;D and wants to play.  Unfortunately we're all pretty busy, so if I'm to get the group together at all it's usually late on a Sunday. After talking to the player he insists it's not the game, or the story, he just happens to be tired. But, it's the same excuse every week, and the odd times we've played at different times or situations, the falling asleep has happened.  How do I cope with:   The morale destroying (for me) idea of your players falling asleep through a campaign and story you've put lots of work into. The general tone of the room when this player loses interest. (Occasionally a couple of others zone out into Facebook when they're not "active" because the players have split up / gone unconscious).   Given that it's an "all or nothing" situation with the group (there are only 3 players and they won't play unless all 3 are around), how do I best deal with it? When clicking continue on the first Boot Camp screen,  I am presented with a dialog that displays:     The startup disk does not have enough space to be partitioned.   You must have at least 39 GB of free space available.     This is despite "About this Mac" reporting 271GB of free space:    And "Disk Utility" reporting 268GB of free space:    Searching online I found  which suggested it was the result of Time Machine which i recently enabled and suggests to run sudo tmutil thinlocalsnapshots / 999999999999 which I did, it ran sucessfully, and I restarted, yet to no avail.  What is the solution to this instance of Apple's poor engineering?  Running macOS High Sierra 10.13.4 (17E202) In Inno Setup is it possible to add conditional statements to what in the [Run] section gets executed? Alternatively is it possible to manually update the built in progress bar? Basically I have 2 MSIs included and using Inno Setup as a bootstrapper, and depending on user input one or both of the MSIs are to be installed.  I have something working using Exec statements in CurStepChanged but it doesn't update the progress bar as the files are extracted and it looks like the installer is stalled.  I guess the end result is I want some progress bar updates while the files are extracted to the temp folder.  The following is my current code:  procedure CurStepChanged(CurStep: TSetupStep); var     ResultCode: Integer; begin     if(CurStep = ssInstall) then begin         if(InstallServer) then begin             ExtractTemporaryFile('ServerSetup.msi');             Exec('msiexec',ExpandConstant('/i "{tmp}\ServerSetup.msi" /qb INSTALLDIR="{code:GetInstallPath}\Server\" ALLUSERS=2'),'', SW_SHOW, ewWaitUntilTerminated, ResultCode);         end;         if(InstallClient) then begin             ExtractTemporaryFile('ClientSetup.msi');             Exec('msiexec',ExpandConstant('/i "{tmp}\ClientSetup.msi" /qb INSTALLDIR="{code:GetInstallPath}\Client\" ALLUSERS=2'),'', SW_SHOW, ewWaitUntilTerminated, ResultCode);         end;     end; end; Why do we need virtual functions in C++? I have two disks in my system:   Non-UEFI windows 10 install UEFI kubuntu 16.10   This system is my home server. I'm migrating from Windows to Kubuntu, but it will take a while since I can't yet duplicate the entire functionality. In the mean time I want to run dual boot so that I can run the server as was (windows) while I'm setting up the Kubuntu deploy in any spare time I get. So:  I'd like to add windows boot to grub's target list, however update-grub does not find my Windows bootloader.  I'm guessing the problem is that it's searching for an EFI boot while there is only a legacy BIOS one.  Is there a way I can add my Windows install as a grub target? Complicated FOR loop nesting. Having trouble cleaning up legacy code I am trying to tidy up some really bad legacy code from an old developer and I'm trying to get rid of these nested for loops. The code below shows what I'm currently working with. I've fixed this before with nested SOQL queries but nothing like this. How would this need to look to remove these for loops (except Trigger.New)? Would I use Maps? How would I do that?  map&lt;Id,SObject&gt; mapProperyIdBudDetail = util.GetObjFields(setPropertyId, 'Property'); map&lt;Id,SObject&gt; mapSpaceIdBudDetail = util.GetObjFields( PropertyMap.keyset(), 'Space');  for ( Lease__c l: Trigger.New ) {      if(mapProperyIdBudDetail.get(PropertyMap.get(l.space__c))!=null) {          lProperties = new List&lt;SObject&gt;{mapProperyIdBudDetail.get(PropertyMap.get(l.space__c))};              for ( SObject p: lProperties ) {                  for ( String fm: FieldMap.keyset() ) {                      if ( p.get(FieldMap.get(fm)) != Null) {                         l.put(fm,p.get(FieldMap.get(fm)));                     }                  }             }     } } I'm starting to write a book on . Since I've been contributing on this tag for a long time, I had the opportunity to read &amp; answer several interesting threads on Stackoverflow related to this technology.  I would like to discuss some of the interesting cases published on Stackoverflow in my book, and I wonder if I could use the images and code shared on those threads in it.  I'm hoping somebody from StackExchange could clarify about the copyright status of the material shared on Stackoverflow questions/answers. Do you have to want to hurt someone for the cruciatus curse to work? OK so the scene where Harry sees Voldemort making Draco tutur Rowel brings a few questions to my mind.      he felt the rage that did not belong to him posses his soul, saw a long room, only light by fire light, and the grate blond Death Eater on the floor,screaming and writhing, and a slighter figure standing over him, wand outstretched, while Harry spoke in a high, cold, merciless voice.   "More, Rowel, or shall we end it and feed you to Nagini? Lord Voldemort is not sure he will forgive you this time...You called me back for this, to tell me Harry Potter has escaped again? Draco, give Rowel another taste of our displeasure... do it, or feel, my wrath yourself!"   A log fell in the fire: flames reared, their light darting across a terrified, pointed white face-   I remember in the Order of the Phoenix Harry tries to do the cruciatus curse on Bellatrix, it doesn't work. She say this is because Harry doesn't mean it, he doesn't want to hurt he enough. If she's right about that (I'm sure she is) I don't see how Draco is managing to make to make Rowel writhe and scream, because it is clear he doesn't want to be doing it.   Also Harry was actually angry at Bellatrix and if his anger at her killing his godfather won't work... well you get my drift.   I know Draco is probably better at magic, but I feel Bellatrix is right, you really have to want them to hurt for it to work.  Next thing, Voldemort's having Draco do it why? Is he doing to upset Lucius, because that and lot of effort to go to, seeing as Voldemort is angry and he'd probably do a better job himself. Or is he trying to train himself a new soldier, I mean the other ones are getting old. iptables port redirect not working for localhost I want to redirect all traffic from port 443 to the internal port 8080. I'm using this config for iptables:  iptables -t nat -I PREROUTING --source 0/0 --destination 0/0 -p tcp \          --dport 443 -j REDIRECT --to-ports 8080   This works for all external clients. But if I'm trying to access the port 443 from the same maschine I'll get a connection refused error.  wget https://localhost   How can I extend the iptables rule to redirect local traffic too?