Is squared Euclidean distance a metric?
Euclidean distance vs Squared
How can I calculate the following sum involving binomial terms:  $$\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$$  Where the value of n can get very big (thus calculating the binomial coefficients is not feasible).  Is there a closed form for this summation? Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$ How to capture a series of screenshots in Web Driver using Java Invalid signature for Kali Linux repositories : "The following signatures were invalid: EXPKEYSIG ED444FF07D8D0BF6 Kali Linux Repository" I am on a MacBook Pro 13 running latest Sierra. I have an external Seagate solid state hard drive that was working and out of the blue stopped working. The only thing on it was my Adobe Lightroom images/videos. Not the LR DB files. I'm sure you have all heard this woe before, so I won't dwell on that. And yes, I back up to the cloud. AWS S3 specifically. Though I am traveling South East Asia for the last year, and staying in cheap hostels. So good internet is hard to come by sometimes. I can't back it up after every export. While most of it is backed up, there is some that is not.  Moving on. The symptoms seems to change every time I plug it in. The first sign was it ejected on it's own. I plugged it in again, and it wouldn't mount. Disk Utility recognized it, so did the command line diskutil list but it wouldn't mount. I rebooted and it worked for a second. Then I could only get to it from the command line. Then trying to frantically back up to my local what was not backed up to the cloud, it all failed. Basically just a cp -R [directory] [local-directory] command.  After some more frantic unplugging and re-plugging plus some command line manual mounts, I finally got it to where the Disk Utility would be able to run first aid on it. It failed. I don't recall the error. So I put it in a freezer. After a few hours I tried again. It is not any better. It still will not mount. Now Disk Utility sees it, but with no partition. I can't even give me information about how much space is used on it.  I have also tried it from a Windows machine. It did not mount. I have tried other cables. No success. As well as tried my other USB port. I also have another working external hard drive exactly like the one giving me issues. It works on all cables and USB ports.  I do have Docker running with a Ubuntu container, I'm trying to think of a way to see if I can try to get to the USB from there. I also have a USB that I have thought about running a live Ubuntu on there to see if I can mount and retrieve the data or fix the HDD that way. But if it will not mount, I doubt these will work.  Can anyone else think of any other tricks I can try myself to see if I can repair this or at least retrieve the data without paying for a service or software? If not, those suggestions are also welcome.  Update   I made the mistake in original post that it was a Solid State Drive. This is my mistake, it is actually a spinning disk hard drive. I bought them long ago and have been traveling with them for so long I just forgot. Question is updated to reflect this. Now diskutil list does not show it at all. The Disk Utility app also does not see it. Based on suggestion from @Allen I seeked out the USB to SATA cable. I did not quite find it, as my options are extremely limited where I am at. Though a local expat on a facebook group was able to help me with a empty 2.5 casing that I was able to extract the drive from original casing and put it in his blank case. It now mounts. Though it has the "click of death" sound to it. And data is not really reachable. While I can ls the directories and Adobe Lightroom does not have the exclamation mark when it can not reach the actual external files. Right clicking on the images and clicking on "Show in Finder" or any other variation of trying to get to the files through Finder or terminal, I have no success. It usually hangs and I get the spinning wheel. Since Adobe Lightroom imports these images into directories named by date, I am going to send the drive off to a data recovery service and ask to recover just unbacked up directories i.e. dates. Next time I will make harder efforts to backup and probably get an actual SSD.   I think this can be closed, due to my low reputation points I can not close this myself. What are the basic rules and idioms for operator overloading? App question timer shouldn't kick in until submission I attempted to ask a question using the iOS app, but it was rejected due to lack of a required tag. On adding the tag I found that I wasn't permitted to submit the question for another 60 seconds, even though this wasn't a new question.  Is this timer intentional, or should it not kick in for edits of questions not actually accepted by the site? How to generate PDF/A and PDF/X? I have heard about PDF  PDF/A (for archival) and PDF/X (for printing). How to generate LaTeX documents like that?  I'm also interested in answers with plain TeX and ConTeXt, and hopefully with both pdfTeX and XeTeX engines. Give an example about limits: $\lim\limits_{x\to0}f(x^{2})$ exists but $\lim\limits_{x\to0}f(x)$ does not. How to create a bootable USB with multiple ISO images in it The app forgets that I voted when I scroll the question Related:   I am using 1.0.71 on KitKat.  Immediately after voting, the arrow is displayed in red and the vote count is correct. However, when I scroll to read answers and then back to the top, the arrow is grey again and the vote count is reset to the previous value.  A reload of the question (pulling the finger down) is needed to show the correct situation, which is kept from then on.  This case was on security.stackexchange.com but I observed the same behavior on other sites too.  Screenshots   original state:  upvoted:  scrolled down and back up  after a reload Formula for coordinates (lat, lon), azimuth and distance. I would like to know how to find a set of coordinates on a small circle some distance from another point.   For example, lets say A = (39.73, -104.98) #Denver  B = (39.83, -106.06) #point approximately 50 nautical miles away from A along the great circle track to C  C = (40.75, -111.88) #Salt Lake City, approximately 323 nautical miles away from A  How do I get the set of orange coordinates when I don't know the angle but I do know the cross track distance?  For concreteness, lets say the outer points near B have a cross track distance of +- 30 nautical miles and the inner points have a cross track of +- 15nm.  And the points near C have a cross track of +- 25 nm.  Also I have an initial bearing from A to C of -1.34 #radians My proof is very different from my reference, hence I am wondering is I got this right?  Apparently, $F$ is continuous, and the identity matrix is closed. Now we want to show that the preimage of continuous function on closed set is closed.  Let $D$ be a closed set, Consider a sequence $x_n \to x_0$ in which $x_n \in f^{-1}(D)$, and we will show that $x_0 \in f^{-1}(D)$.  Since $f$ is continuous, we have a convergent sequence $$\lim_{n\to \infty} f(x_n) = f(x_0) = y.$$  But we know $y$ is in the range, hence, $x_0$ is in the domain. So the preimage is also closed since it contains all the limit points.  Thank you. On the canonical isomorphism between $V$ and $V^{**}$ Picklist dependent on 2 controlling picklist I have 3 picklist in an object Test1, Test2, Test3  1. Test2 is dependent on Test1  2. Test3 is dependent on both.. Test1 and Test2    I want to have Test3 picklist showing values accordindly. i.e  if U selected Test1 = First and Test2 = SA . I should be able to see "IST,ABC and PQR" in Test 3.   Is this possible??? Why is it a bad practice to lock the object we are going to change? See dashboard as non logged user in community Is it possible, as a non logged user, to see report and dashboard in community when it is open to non logged user? And  for analytic dashboards? What is your simplest explanation of string theory? Do messages in archive count to your inbox space? Pretty much as the title says, do messages in archive count to your total inbox space? In Ubuntu, I want to open a PDF document generated for Adobe Reader 10. Apparently the latest version which I can install is Adobe Reader 9.5.5. Is there a way to install version 10?  I installed Wine, but I don't know how to install acroread using Wine.