The summation of reciprocal of factorial of number $$\lim_{n\to \infty} S_n=\lim_{n\to \infty}\sum_{k=1}^n\frac{1}{n!}$$  I need to show that this series is a convergent series. How do I show this series to be convergent? My book says that this is convergent. Please provide sone hint.
How to check if $\sum_{n=1}^\infty \frac 1{n!}$ is converging or diverging by direct comparison test? $$\sum_{n=1}^\infty \frac 1{n!}$$   I think we may compare it with $\frac{1}{n^n}$, and say that $\frac{1}{n!}&gt;\frac{1}{n^n}$. But I am not sure of the convergence or divergence of $\frac{1}{n^n}$ itself, so this turns out to be useless.  What other way is there?
I have this table but check constraint is throwing me an error:     Column CHECK constraint for column 'MedicamentRegulated' references another column, table 'Medicaments'.   I've seen this as allowed in SQL Server but I don't know why it doesn't work :/  CREATE TABLE Medicaments ( MedicamentID INT NOT NULL IDENTITY(1,1) PRIMARY KEY, Name VARCHAR(50), DateValidity DATE, MedicamentRegulated BIT CHECK((MedicamentRegulated = 1 AND DateValidity IS NOT NULL)    OR MedicamentRegulated = 0) ) Short story with competitors complaining to government about a new very popular synthetic food Unable to change payment information to NONE in iOS Appstore Ever since adding an iTunes gift card to my account, I'm getting verification requests like crazy. I can't even download free apps. It takes me to my payment info and when I try to select none, I continually get a message under the payment info that says "you must verify your payment info to continue"  I don't want a credit card on file and would really like the none option to work. My ID shows I still have iTunes credit. How can I set custom key bindings and key macros on Mac OS X? I recently upgraded to Snow Leopard, from Leopard and I was using an awesome app called  that let you remap your keys, set scripts/macros and even had repeat functionality.   However, this app doesn't seem to be in active development anymore, and 10.6 broke the ability to bind certain modifier keys (Shift) with other keys.   I totally miss things like Shift+Insert for paste (Linux/Windows), setting Ctrl+Shift+Esc for Activity Monitor, and Ctrl+Alt+Del for the login window.   So, how can I achieve this instead? As I was trying to validate our pcb design, I measured the impedance matching on the digital transmission lines, and got stuck with the oscilloscope not showing what I expected. We are using the PicoScope 4227, but I suspect that the strange measurement is not directly related to the specific oscilloscope but more to general on how to measure digital signals.  My setup is as follow: I measure the output-pin of an FPGA with both oscilloscope input A and B.  Input A (blue) is measured using the oscilloscope probe set to x10.  Input B (red) is measured using a 50-ohm coxial cable terminated at the scope input with 50-ohm.  As you can see, Input B seems correct, no reflection ect.  But Input A (the probe) has some overshoot, and ringing.  The probe should be calibrated and valid to 250MHz, so I don't get was is wrong. ?  I suspect that the small probe-clip adds some inductance, and therefore we see the ringing. But I really don't know.    EDIT After reading your answers, I walked got into our lab storage and started looking, and found a probe GND clip like the one showed in the answer below.   When I use that clip, I get the output below. Which is really a huge improvement. Cannot log into Area 51 with OpenID I recently tried many times to log into Area 51 with my Stack Exchange OpenID. Each time, I got this:    Then, I went to my OpenID account, and I saw this:    ...what is going on??  I have chrome, and extensions that block 3rd party cookies... is that the problem? Outcast boy meets girl underwater Here's another one I can't find, but somebody will probably recognize right away. A young man has been thrown out of respectable society. To make sure he stays away from people (and they stay away from him), those who have condemned him alter his body so that he always smells bad. Of course, no one can smell underwater - and that's where he meets a girl, while they're both swimming underwater in a swimming pool. I don't remember a lot of details about this story - but I remember the main character was not very nice - he was often mean to other people. Whether he'd always been like that, or whether his nastiness was because everyone had rejected him, I can't remember. I would have read this story in the mid-seventies, but it was probably written earlier. Finding the radius of convergence for $\sum_{n=0}^{\infty} \frac{(n!)^kx^n}{(kn)!}$ I'm reviewing some calculus concepts right now, and this series stumped me. I'm trying to figure out what its radius of convergence is, but it's not falling for any of my old tricks. Using the root-test, I want to compute: $$ L_1=\lim_{n\rightarrow\infty} \left|\sqrt[n]{\frac{(n!)^k}{(kn)!}}\right| $$  where $k$ is some positive integer. Passing the limit through the absolute-value bars and $n$th root symbol, I now want to compute the simpler (?) $$ L_2 = \lim_{n\rightarrow\infty} \sqrt[n]{\frac{(n!)^k}{(kn)!}}$$  Which I can't seem to pin down. Numerical tests indicate it goes to 0, and that jives with an intuitive notion I have that there are always $k$ terms on the numerator, but $kn$ terms in the denominator. But since all of these terms themselves depend on $n$, proving that $L_2 = 0$ escapes me. Once we get this result (if it's correct), then clearly $L_1$ is also 0, and the radius of convergence of the series is $\mathbb{R}$. Thanks for any ideas you may have. Custom DataTable using Vanilla Datables in LWC I'm trying to build a custom datable because I want the functionality to sort, search and paginate and also add action buttons in each row. Initially, my VF page was using  but we have now decided to rebuild that page in LWC.  I found a similar  but it hasn't really worked for me.  I then found  (Javascript) and  (ES2018) I have tried to implement Vanilla Datatables but I keep running into issues such as:      TypeError: Cannot read property 'length' of undefined   The above error is thrown because the library is unable to find the body of the table.   My point is that I feel this library won't work because it's using document, window and so on.   I was wondering if there is a way I could convert this library to something that is more suited to LWC basically have it "export" the modules. Since I'm not a JS expert I'm unable to put the pieces together.   Just for some context, I'll post my code here:  &lt;template&gt;     &lt;table class="sobject-table slds-table slds-table_cell-buffer slds-table_bordered"&gt;         &lt;thead&gt;             &lt;tr class="slds-line-height_reset"&gt;                 &lt;template for:each={fieldSetData} for:item="field"&gt;                     &lt;th key={field.apiName} title={field.fieldLabel} class="" data-scope="col"&gt;                         &lt;div class="slds-truncate" title={field.fieldLabel}&gt;{field.fieldLabel}&lt;/div&gt;                     &lt;/th&gt;                 &lt;/template&gt;             &lt;/tr&gt;         &lt;/thead&gt;         &lt;tbody&gt;             &lt;template for:each={records} for:item="row"&gt;                 &lt;tr key={row} class="slds-hint-parent"&gt;                     &lt;template for:each={row} for:item="data"&gt;                         &lt;td key={data.id} data-label="Name" data-scope="row"&gt;{data.value}&lt;/td&gt;                     &lt;/template&gt;                 &lt;/tr&gt;             &lt;/template&gt;         &lt;/tbody&gt;     &lt;/table&gt; &lt;/template&gt;   import {LightningElement, api, wire} from 'lwc'; import {processRecords} from 'c/recordGenerator'; import getFieldSetData from '@salesforce/apex/FieldSetData.getFieldSetData'; import getSobjectRecords from '@salesforce/apex/DeomoCTRL.getRecords'; import VanillaDatatable from '@salesforce/resourceUrl/VanillaDatatable'; import {loadScript, loadStyle} from 'lightning/platformResourceLoader';  export default class ManageSelectedIndicators extends LightningElement {     @api recordId;     records;     fieldSetData;     @wire(         getFieldSetData,         {objectName: 'SOBJECTName', fieldSet: 'FIELSETName'}     ) wiredFieldSetData({error, data}) {         console.log('wired called in Child')         if (data) {             this.fieldSetData = data;             this.getData();         }     }       constructor() {         super();         console.log('Constructor called in Child');     }      connectedCallback() {         console.log('Connected callback');     }      renderedCallback() {         console.log('Rendered callback');         Promise.all([              loadScript(this, VanillaDatatable + '/VanillaDataTables/src/vanilla-dataTables.js')          ]).then(() =&gt; {              const table = new DataTable(                  document.getElementsByClassName('.sobject-table'),                  //Also tried this.template.querySelector('.sobject-table'),                  {searchable: true, sortable : true}              );          })          .catch(error =&gt; {             console.log(error);          });     }      getData() {         getSobjectRecords ({             sobjectId: this.recordId         })         .then(response =&gt; {             this.records= processRecords(response, this.fieldSetData);         })         .catch((error) =&gt; {             console.log(error);         });     }  }   Edit: I have also tried lwc:dom="manual" that didn't seem to work either.  Is there any other way I could achieve these functionalities? Or do I have to write custom code to achieve this? I needed to change the SID of an Oracle XE database (not the Service Name) to match a production database.  When I tried searching online, most of the pages were describing changing or adding a service name through tnsnames.ora; that's not what I needed to do. What if the LHC doesn't see SUSY? A question in four parts.   What are the main problems which supersymmetry purports to solve?  What would constitute lack of evidence for SUSY at the proposed LHC energy scales (e.g. certain predicted superpartners are not in fact observed)?  Are there alternative theoretical approaches which would address the SUSY problem set and which would still be credible in such an LHC no-SUSY-scenario? Where would LHC-disconfirmation of SUSY leave String Theory?   I would like to think that these four points could be taken together as one question. What are the grammatical rules determining whether to use "which" or "what"? What are the grammatical rules determining whether to use which or what?  I usually go by intuition. It's "What car are you looking at?" and "What bicycle do you like most?" but "Which song did you sing?" Quite often, I don't know whether to use what or which.  How can I tell? How to install driver for TP-Link TL-WN722N(EU)V2 on Ubuntu 17.04 Kylin I can not install the TP-LINK WN722N V2, which includes a 8188 EUS chip. Then I tried to install the backports v4.4.2,but   do not want to recognize either.  The TP-Link driver installation errors thrown out:  man@kman-livve:~$ cd '/home/kman/Documents/Tplink 722 N V2/rtl8188EUS_linux_v4.3.0.8_13968.20150417' kman@kman-livve:~/Documents/Tplink ...$ sudo make  "******************************************" "NO SKRC,we will use default KSRC" "******************************************" make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/4.10.0-15-generic/build M=/home/kman/Documents/Tplink 722 N V2/rtl8188EUS_linux_v4.3.0.8_13968.20150417  modules make[1]: Entering directory '/usr/src/linux-headers-4.10.0-15-generic' arch/x86/Makefile:140: CONFIG_X86_X32 enabled but no binutils support make[1]: *** No rule to make target '722'.  Stop. make[1]: Leaving directory '/usr/src/linux-headers-4.10.0-15-generic' Makefile:1367: recipe for target 'modules' failed   A method to know him, I do not know about. Thanks  Model:TL-WN722N(EU)_V2_161112_Linux.zip Chipset:rtl8188EUS_linux_v4.3.0.8_13 What does ;; do in sh? error in running bash script as root I have a simple shutdown script which i want to run as root  shutdown -h +30; echo "succesfull";   I have followed these answer, to make my script root.  first I run this command  sudo chown root.root $HOME/test/test.sh sudo chmod 4755 $HOME/test/test.sh   and then made changes in sudoers  sudo visudo   added this command after this line %sudo   ALL=(ALL:ALL) ALL  eka ALL=(ALL) NOPASSWD: $HOME/test/test.sh   But when i executed my script its showing this error  shutdown: Need to be root succesfull What is the right way to consistently mangle bash terminal? I'm on OSX 10.11.1 and occasionally my bash terminal gets mangled. It often happens when I accidentally cat a binary file. The result can be seen on the image below. The output becomes weird, and I can't type ascii characters anymore.    Even though this happens occasionally, I couldn't find a way to consistently reproduce the issue. Online search recommends doing cat /bin/*, but that works sporadically, only after a couple dozen tries.  I want to do this so I can find an easy solution how to handle this in tmux.  How do I consistently get bash to a "mangled" state? Is there maybe a magic unicode character that can do this? Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$ how to get user permissions for nfs share? Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$ Is there a function to round a float in C or do I need to write my own?       float conver = 45.592346543;   I would like to round the actual value to one decimal place, conver = 45.6.