$$\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}$$  I know that with infinite square roots it's $x = \sqrt{2 + x}$, but what about a non-infinite number of roots? I've searched around a lot for this, and can't find anything useful, nor can I make a dent in the problem myself.   Maybe I'm searching using the wrong vocabulary?
so I stumbled upon this equation/formula, and I have no idea how to prove it. I don't know how should I approach it: $$ \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{\vphantom{\large A}2\,}\,}\,}\,}\ =\ 2\cos\left(\vphantom{\Large A}\pi \over 2^{n + 1}\right) $$  where $n\in\mathbb N$ and the square root sign appears $n$-times.  I thought about using sequences and limits, to express the LHS as a recurrence relation but I didn't get anywhere.  edit: Solved, thanks for your answers and comments.
why does fdisk add one additional sector when creating partitions? I'm playing around with fdisk and I tried to create a partition on an empty USB drive. Here's how that went: Command (m for help): n Partition number (1-128, default 1): 1 First sector (34-61187102, default 2048): 2048 Last sector, +/-sectors or +/-size{K,M,G,T,P} (2048-61187102, default 61187102): +30000000           Created a new partition 1 of type 'Linux filesystem' and of size 14,3 GiB.  so just one partition with 30 million sectors. However, when I check how many sectors it contains I get:  I'm checking with a different program and I see again that additional sector:  Sorry for the pettiness :) I'm learning. my email limit is exceeded after sending 10-12 emails..what could be the problem..as i have seen the limit is 1000 emails/day.i am not able to find out what could be the problem..Can some give me some suggestions. As i also know we can send 10 emails in a single transaction.I am sending emails in a batch class.  I am calling this batch class on button click and filling emailList with emailsId's.                      String query='Select id from Lead';//No use of this query                     Batch_send_emails bse=new Batch_send_emails();                     bse.query=query;                                                         bse.resendEmails=emailList;                     database.executebatch(bse);           **Batch Class**           if(!resendEmails.isEmpty())           {               for(String s:resendEmails)                {                   emailsLeads.add(s);                }           }           Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();         mail.setToAddresses(emailsLeads);        // mail.setCcAddresses(ccAddresses);         String subject='GoToMeeting Invitation Details for '+subject;         String body='test';          mail.setHtmlBody(body);          mail.setSubject(subject);         Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });          } In TeX, how is computing zero sign written with slanted vertical line on it? How do I access a page's HTTP response headers via JavaScript?  Related to , which was modified to ask about accessing two specific HTTP headers.     Related: Ackermann Function primitive recursive "This question is not available, it may have been deleted" when submitting a question on the Android app after losing internet connection Recovering broken or deleted NTFS partitions About two weeks ago I had a problem with my PC that my brother wrote a question about at .  I still haven't solved the problem, so my PC is unusable now.  Now I think that it would be simpler to re-install both Win7 &amp; Ubuntu than repair them, but there're some data on their partitions. I want to recover this data.  These partitions are not mountable for some reason. I don't know why.  sudo fdisk -l about the problematic partitions:     Device    Boot      Start         End      Blocks   Id  System /dev/sda1            2048     147912703    73955328   83 Linux /dev/sdb2            206848   174079999    86936576    7  HPFS/NTFS/exFAT   And in GParted:      And the error of the mount command:  Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   And the exact same message for /dev/sda1  How can I recover my data from those HDDs?  EDIT     I have tried to specify the type of the drive:  $ sudo mount -t ext4 /dev/sda1 /olddisk mount: wrong fs type, bad option, bad superblock on /dev/sda1,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so $ sudo mount -t ntfs /dev/sdb2 /olddisk NTFS signature is missing. Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   EDIT     sudo ntfsfix /dev/sdb2 returns:  Mounting volume... NTFS signature is missing. FAILED Attempting to correct errors... NTFS signature is missing. FAILED Failed to startup volume: Invalid argument NTFS signature is missing. Trying the alternate boot sector Unrecoverable error Volume is corrupt. You should run chkdsk. I have a featureclass in an Esri file geodatabase. When I edit the features using the editor in ArcMap, and I delete most of my features and keeping only the ones in the middle, the zoom to layer command doesn't work as expected. Instead of zooming to the extent of the features remaining in the feature class, the extent will be the former one (containing all deleted features). When reviewing the extent values in the properties dialog for the feature class, I can clearly see the old values. So the edit session doesn't seem to alter the full extent values.  Is there a way to recalculate these values?  I am pretty sure that this problem should occur to everyone editing features in ArcMap... How to avoid long nesting of asynchronous functions in Node.js I want to monitor private message and want to check and store at admin side. so admin can see who doing message to whom and make the policy for to sending the message. Looking to identify a short story I read in a sci-fi anthology as a child, about an angry, bullied somewhat misanthropic boy who is given immense near-omnipotent powers by an alien intelligence. I read this in English, sometime in the late 1990s/early 2000s. He goes on to use this power to destroy the human race, which causes him to age terribly in a very short amount of time. At the end of the story he is a lonely old man stripped of the powers he held briefly, and is alone on an isolated Earth. The aliens then proceed to invade Earth. Evolutionary chronology - if any, which species have evolved in the last 100 years I heared somewhere, I cannot remember where, that there has not been an evolution observed in our lifetime. In life science class, right at the start, we was doing the usual MRSGREN (how to tell if something is a living organism), and the tutor said that you can also tell something is a living organism if it evolves. So I asked if there has been an observed evolution in our lifetime. She said that there had been many but could not recite any off the top of her head, so the next week she handed me a piece of paper with 8 or so websites that aparrently corroborated her claim. I have not got the paper anymore but I recall there been on there the peppered moth or something. So I set out to look for a chronological list of evolution but could not find an authoritative one. I could only find something on wikipedia that indicated that species have been dying out for the past thousand years, but nothing saying that any have evolved. CString to char* We are using the CString class throughout most of our code. However sometimes we need to convert to a char *. at the moment we have been doing this using variable.GetBuffer(0) and this seems to work ( this mainly happens when passing the Csting into a function where the function requires a char *). The function accepts this and we keep going.  However we have lately become worried about how this works, and whether there is a better way to do it.  The way i understand it to work is it passes a char pointer into the function that points at the first character in the CString and all works well.  I Guess we are just worried about memory leaks or any unforseen circumstances where this might not be a good idea. Relativistic Mass and Dark Matter In a question  Ron Maimon comments that "relativistic mass makes gravity, not rest mass."  If so, does that mean that the faster that stars orbit the galaxy the larger the relativistic mass of the galaxy therefore more gravity therefore the stars orbit even faster therefore the gravity gets even more therefore the stars keep on getting faster ...  So the speed of stars and mass of galaxy would be correlated with age and history of the galaxy or galaxy clusters and that's why calculations of galaxies' masses don't add up. Javascript && operator as if statement? If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime. Update:   Once upon a time there was a feature called . Its goal was to help our most active users find the questions they can answer. &quot;New nav&quot; never made it out of beta and that beta only ever made it to Stack Overflow users. Several months ago we gave new nav a sad, but overdue burial. As we promised, we've been working on a replacement for new nav, and now it's time for us to start rolling it out. We're calling it custom question lists and we are really excited about its potential to help all users get at the questions that are most interesting to them. While we hope what we've built hits the mark for many of you who have requested a feature like this (e.g., , , , , , ), we know how difficult it is to make something complex simple. So, we are rolling this out in beta to gather feedback from you and iterate on it. (Don't worry, we promise to actually release it this time.) When it's live later you'll be able to opt-in to the beta by turning on a new account preference. This will enable the feature for Stack Overflow, Meta Stack Overflow, and Meta Stack Exchange. It will be available for all network sites when the beta period is over. Schedule for future improvements This feature will roll out in four phases:  Phase I: Filter and sort controls to let you modify a question list view (Julyish) Phase II: Saved custom lists (In progress, ETA November 2018) Phase III: Notifications on custom lists (December 2018) Phase IV: Final fixes and official release (January 2019)  Sneak peak Phase I: Filter and sorts We'll add filter and sort controls to question lists. This does two things:  Clarifies the definition of built-in views - Naming is hard and short names can't always describe what a view is showing you. By exposing the filter and sort controls it is more obvious. Introduces the ability to create new custom views - This won't be super useful until we add the ability to save the views to the UI (phase II). Until then you can bookmark the URL and get back to your views.  Question list with new controls   Views drop down   Filter   Sort   Phase II: Saved custom question lists In this phase we will add the ability to save your custom questions lists. Create custom list In our current design, a dialog will be pre-populated based on the filters and sorts you're currently using. Give it a name, confirm your options, and click save.  Accessing your saved lists When you save your custom lists they will show up in the &quot;More&quot; drop down for question list views. Additionally, you can add them to the left navigation bar for easy access (see image below).  Phase III: Notifications For phase III we'll enable indicators for when new items are available in a custom question list. When you pin a question list to the left nav you can see a dot on any list with new items.  Feedback welcome As usual, we're interested in your constructive feedback. This is a work in progress and, as mentioned, will be rolled out in phases. You can provide feedback on the concepts now based on the information in this post and provide feedback based on the working elements as they are released. I am used to see timestamp everywhere by it's color. The recent timestamps are a little bit reddish everywhere. E.g. in Meta Stack Overflow:  Last edit:        Last seen:        But in Meta Stack Exchange they have same color everywhere even for recent time:  Last edit:        Last seen:         Please make it something like this: Switch off Windows Update for a particular program or feature I'm getting really tired of unchecking the same Windows Update candidates so save hundreds of MB's of dowbloads, especially for programs I never use, that are in fact not even installed, and those I don't wish to update.  Is there any way to permanently, or until another explicit change, to turn off certain updates?  There is an option called 'Hide update', but that unsettles me a bit. Below is my code to create the component dynamically - The component is "ui:inputselect"  $A.createComponent(             RecoveryLineItem.Attributes[i].name,{                 "class" : "slds-input ",                 "aura:id" : 'ExampleId',                 "label" : RecoveryLineItem.Attributes[i].label,                 "multiple" : RecoveryLineItem.Attributes[i].multiple             }, ....   ..  console.log(component.find('ExampleId').get("v.value"))    Or console.log(component.find('ExampleId'))  is Giving as 'Undefined"  How to access the aura:id of the dynamically created components?