is there an explicit definition of the following sequence? $$s(n)=\sum_{i=0}^n \frac1{i!}$$ Sincerely
Is there a closed form solution for the following series? (Without Using Gamma Function): $$ S=\sum _{i=1}^{n-1} \frac{1}{(i+1)!} $$
How can I use a variable in the replacement side of the Perl substitution operator? I would like to do the following: $find = &quot;start (.*) end&quot;; $replace = &quot;foo \1 bar&quot;;  $var = &quot;start middle end&quot;; $var =~ s/$find/$replace/;  I would expect $var to contain &quot;foo middle bar&quot;, but it does not work. Neither does: $replace = 'foo \1 bar';  Somehow I am missing something regarding the escaping. How can I specify a long list of math operators? The preambles of my LaTeX documents often include many many lines of \DeclareMathOperator instructions, e.g.  \DeclareMathOperator{\Rep}{Rep} \DeclareMathOperator{\Tet}{Tet} \DeclareMathOperator{\Maps}{Maps} \DeclareMathOperator{\Diff}{Diff}   Is there a nice way to map some macro over a list, so I could do this more concisely, and with less copying and pasting when I add a new math operator? How to stop Katoolin from crashing Ubuntu? I updated from 14.04 to 16.04 and used katoolin to add some Kali tools. After restart, the boot up of Linux ran codes, but stopped at a certain point never to load login. So I reinstalled 16.04, ran updates and tried again. This time, the boot menu was changed to Kali as well as the OS name (I'm using Windows 7 dual boot with Ubuntu); login started in Ubuntu style without user name, had to type in the name... then it goes to the logo screen never to log in.  How can I use katoolin without it affecting the boot menu interface? Does this happen when the user selects the option 'add Kali repositories and updates'? Are the Kali repositories necessary? I'd much rather just install the tools and not mess with the Ubuntu interface. After Windows 10 Fall Creators Update, a svchost.exe instance is constantly using CPU time Since installing the Windows 10 Fall Creators Update, I have a svchost.exe process that is constantly using about 14​ % of CPU time:    This svchost.exe instance is responsible for hosting three services:    The CPU time is consumed by a thread inside that process that  cannot attribute to any of these three services:    Given that these three services are considered critical system services, it's hard to do anything about them. These services cannot be stopped or disabled by services.msc, and terminating the process triggers a bugcheck (CRITICAL_PROCESS_DIED). Disabling the Windows Defender Firewall through the settings UI does not reduce CPU usage.  I'm out of ideas. What could be causing this? How can I debug this further? Is there a workaround to stop these services?    Update: After some debugging with , we've isolated this to the Windows Defender Firewall service. Process Monitor shows that it's constantly accessing the registry:    A CSV export of a Process Monitor capture, filtered to that process, is available .  I’m still looking for a way to stop that behavior.    Update 2: Analysis with the Windows Performance Analyzer shows that most CPU time is consumed by code from rpcrt4.dll: I am learning Linux and I was trying the gzip command. I tried it on a folder which has a hierarchy like  Personal/Folder1/file1.amr Personal/Folder2/file2.amr Personal/Folder3/file3.amr Personal/Folder4/file4.amr   I ran     "gzip -r Personal" and now its like  Personal/Folder1/file1.amr.gz Personal/Folder2/file2.amr.gz Personal/Folder3/file3.amr.gz Personal/Folder4/file4.amr.gz   How do I go back? "To work for" vs. "to work in" vs. "to work at" Is the preposition in universal in conjunction with the verb ‘to work’ and can it be used with any organizations and businesses?  For example:        He works as a cook in a local hotel near here.   He works in an office in Chicago.   She works in a big company.   She works in the emergency unit at the hospital.   She works in a shoe repair shop.   After leaving school, he worked in a restaurant for a year. military hospital.   His sister works in a bank.   She works in a shoe factory.   He works in a steel plant.   She works in a gift store on weekends.   Ann works in a research institute.      When should the prepositions at and for be used? For example:        Barbara works at a travel agency.   She works at the local supermarket.   Now he works for a bank.   I work for a small non-profit organization.      I’ve never heard:     She works for a shoe factory.   But with a law firm it’s OK:     She works for a law firm.   Why? Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets? Best vehicle for each stage in Hill Climb Racing In Hill Climb Racing we have several vehicles and several stages.  Different vehicles have different performances on the same stage, and I'd like to know what are the best combinations to maximize distance in each stage.    Also, what is the best combination of a vehicle and a stage to get lots of coins? Noise in JPEG file after processing RAW file in photoshop Recently i started shooting in RAW after understanding its advantages over JPEG format.   While processing the RAW file there is an option to reduce noise in a captured picture. It works great when i am working on RAW file. But as soon as I save file in JPEG format, noise comes back.  I understand that while converting from RAW to JPEG compression techniques will be applied. But how can i handle this situation (while doing post processing)? How to correctly post a Q&A style question (i.e.self answer) without it failing minimal understanding As I understand it Q&amp;A style questions are  but a self answered question should be judged independently of the answer. Often after I've solved a problem I would like to share the question and answer on stack overflow (and have on a couple of occasions) but how to show &quot;minimal understanding of the problem&quot; is always challenging. For example I have been looking into the following question  How can I plot a straight line in the JMonkey Engine library I'm trying to plot straight lines between vertices that I specify using the JMonkey Engine 3D graphics library. So for example if I was to try to plot between: (2,0,0) (-1,0,1) (0,1,1) (1,1,1) (1,4,0) Then I would get:   This is something I do (and forget how to do) relatively often and the answer is harder to find than you'd imagine ( provides everything needed to figure it out but its spread out over several posts and isn't a complete solution on its own). Therefore I want to provide a Q&amp;A for it but at present this question feels like it would fail the minimal understanding test  Questions must demonstrate a minimal understanding of the problem being solved. Tell us what you've tried to do, why it didn't work, and how it should work  Should I make up some imaginary problem? (Probably the final source code messed up a bit) Or mention in the question that I’m self answering to assuage some of the normal &quot;This is not a do your work for you site&quot; comments. "Parsing filters unsupported" error during extraction of RAR file I have received an .rar which I wish to unpack as it contains something rather important to me that I need to really have now. However even though I can view the contents of the .rar archive in the Archive Manager, I am unable to extract it due to this error:    The archive should contain two folders within it, each though contain at least 10 audio files as well as a PDF file each (I don't know what the contents exactly should be except for there should be audio files in there, and the content I have described is what I can see from the Archive Manager's view). So the only thing I am left with except the error is one of the folders and one of the audio files, but it says it has 0 bytes in it.  So how exactly do I fix this problem? I am running Ubuntu GNOME 16.04.1 with GNOME 3.20.  Information Update:  In reply to a comment requesting the output from the dpkg -l unrar unrar-free command:  Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name           Version      Architecture Description +++-==============-============-============-================================= un  unrar          &lt;none&gt;       &lt;none&gt;       (no description available) dpkg-query: no packages found matching unrar-free Answer draft is lost if you click to sign up When writing an answer on a site where you don't have an account or are not logged in, below the answer entry textbox are options to create an account or continue as guest by providing a nickname and email. I had written an answer of several paragraphs on a network site, clicked &quot;Sign up with Google&quot; (resulting in association to my existing network-wide profile) but after doing so instead of showing my answer to be posted, only the first five or six words were retained.  I know that I had no account on this site previously because I just received the association bonus... I cannot tell whether the bug also affects totally new users or those with accounts but who are not logged in. This is a very unwelcoming user experience.  Please fix it. If the intended workflow is to click &quot;Post Answer&quot; first and associate the account afterwards, then the sign up options should not be shown until the answer is posted, and certainly not above the Post Answer button. This problem also occurs if you already have an account on the site, and click 'sign up with google' (which allows you to successfully log in). It should be trivial, and it might even be in the help, but I can't figure out how to navigate it. How do I indent multiple lines quickly in vi? Formula for calculating $\sum_{n=0}^{m}nr^n$ I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks! Markdown + Mathjax => PDF I've used LaTeX a lot in the past, but now, when comparing with StackExchange's great , I find it tedious, for short documents (&lt; 2 pages), to have to use pure LaTeX. For a short document, instead of having 30 lines as introduction: \begin{document} \documentclass[11pt,a4paper]{article} \usepackage[frenchb]{babel} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts}  + &lt;lots of other things&gt; ...  I'd like to write my short document with MarkDown + Math, like on . Question: Is there an offline compiler such that compilemarkdown exercice.tex  would produce a PDF from this: #Title  Here is a *short document* including Markdown and Math, here is the equation:  $$f(x)=x^2$$  ___  Proof: ...   This is **bold**. Uncountable sets of Hausdorff dimension zero Let $A \subset \mathbb{R}$ be a countable set.  It is easy to see that $A$ has Hausdorff dimension $\dim_H(A) = 0$.  Do there exist uncountable sets $A \subset \mathbb{R}$ with $\dim_H(A) = 0$? Remove impossible badges from per-site metas Per-site metas lists some badges that are impossible to get. For example  lists:         But these are impossibly to get because per-site metas do not support bounties, were not in a beta stage or Area 51 proposals. I therefore suggest that these badges are removed from the per-site metas. They have no function and they are confusing. There are already badges that are unavailable on per-site metas but available on the main sites:    Convention Quorum  This seems to suggest that per-site metas should only contain badges that can be possibly awarded. How can I obfuscate (protect) JavaScript? I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? Batch renaming files I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this?