I was constructing a proof through inequalities, but I am having a bit of problem showing the following step:  $$\sum_{k=N+1}^\infty \frac {1}{k!} &lt; \frac {1}{N!}$$   Is there any quick way to show this?
Prove that:  $$\displaystyle \sum_{n=m+1}^\infty \dfrac{1}{n!} \le \dfrac{1}{m\cdot m!}$$  I have tried induction on $m$ but it does not work very well. Any suggestion?
$c$ is a complex number that satisyfing $(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$ Let $c$ is complex-number satisfying :  $(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$  So, how could i get $(3c^{100}+\frac{2}{c^{100}}+1)(c^{100}+\frac{2}{c^{100}}+3)$ ? Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.   I thought I would do the following ... As $n$ is not divisible by $2$ and $3$ then $$n=2k+1\;\text{or}\\n=3k+1\;\text{or}\\n=3k+2\;\;\;\;$$for some $n\in\mathbb{N}$. And then make induction over $k$ in each case.$$24\mid (2k+1)^2-1\;\text{or}\\24\mid (3k+1)^2-1\;\text{or}\\24\mid (3k+2)^2-1\;\;\;\;$$This question is in a text of Euclidean Division I'm reviewing, and I wonder if there is a simpler, faster, or direct this way. PHP Echo Line Breaks If $P(|X-19.1| \leq a) = 0.98$ then why is it necessarily $P(\frac{X-19.1}{17} \leq \frac{a}{17})= 0.99$? If in a UFD every maximal ideal is principal then it is a PID How to convert java.util.Date to java.sql.Date? I am trying to use a  as input and then creating a query with it - so I need a .    I was surprised to find that it couldn't do the conversion implicitly or explicitly - but I don't even know how I would do this, as the Java API is still fairly new to me. Motivation behind the definition of ideal class group Design for Facebook authentication in an iOS app that also accesses a secured web service Combinatorics identity question I encountered this particular combinatorial identity :$$\begin{align}&amp;1\dbinom{n-1}{r-1}+2\dbinom{n-2}{r-1}+\cdots+(n+1-r)\dbinom{r-1}{r-1}\\=&amp;\dbinom{n}{r}+\dbinom{n-1}{r}+\cdots+\dbinom{r}{r}\\=&amp; \dbinom{n+1}{r+1}\end{align}$$How does one figure it out? Printer service not found on port 515 For services list on my Ubuntu, Printer service not found on port 515.  nmap -sT -O localhost  PORT     STATE SERVICE 23/tcp   open  telnet 139/tcp  open  netbios-ssn 445/tcp  open  microsoft-ds 631/tcp  open  ipp 9050/tcp open  tor-socks Device type: general purpose Running: Linux 3.X OS CPE: cpe:/o:linux:linux_kernel:3 OS details: Linux 3.12 - 3.19, Linux 3.8 - 3.19       There is no Printer service on port 515. How to add Printer service on port 515?     nmap -v -p 515 127.0.0.1  Starting Nmap 7.01 ( https://nmap.org ) at 2016-11-19 13:03 IRST Initiating SYN Stealth Scan at 13:03 Scanning localhost (127.0.0.1) [1 port] Completed SYN Stealth Scan at 13:03, 0.21s elapsed (1 total ports) Nmap scan report for localhost (127.0.0.1) Host is up (0.000065s latency). PORT    STATE  SERVICE 515/tcp closed printer Create Case thread Id using Apex (SOQL limit-proof) There are many posts about creating Case threadIds with Apex, notably   As the posters have noted, the SFDC rules of the threadId are subject to change over time and the only reliable way that I've seen is to do   // To be replaced with a real case Id. Id caseId = '500c0000008kJL5';   List&lt;Messaging.RenderEmailTemplateBodyResult&gt; renderResults =   Messaging.renderEmailTemplate(null, caseId, new List&lt;String&gt;{'{!Case.Thread_Id}'});  System.debug('this is the Case Thread Id: ' + renderResults[0].getMergedBody());   HOWEVER ... The method call Messaging.renderEmailTemplate burns a SOQL ()  So you can't prepopulate your Cases in an afterInsert or beforeUpdate Trigger because a transaction can be up to 2,000 (Platform Events), up to 10,000 (direct Apex DML) or more, typically, 200 rows.  All of these are > 100 SOQL limit.     So, before I go to the trouble of doing this in a chained set of async   tasks; is there more recent thinking on this subject of creating ThreadIds? I am running out of storage, I usually have bought a lot of my games on disk but if I buy a game on the store then delete it, and want to redownload it do I have to buy it again Movie with killer androids (glowing eyes, screaming) What communication can be intercepted by network I'm connected over VPN to? I have to connect to client's network over VPN, and I was wondering if the client can intercept (and read) my Google Talk messages (or any other IM communication) while I'm VPN-ing.  My main concern is them having access to our internal conversations.  Suggest workarounds if you have any. I read on  that the netbook edition of Ubuntu was discontinued and that it is now integrated into the main distribution (as of 11.04).  I tried 11.04 on my new Samsung NC110-A06AU with 10.1" 1024x600 display. Most things worked out of the box, but some (like backlight power control) needed some  before they began to co-operate.  One thing that seems to be an ongoing problem is the resolution.  At 1024x600, most of the dialogue boxes run off the bottom of the screen, including the update manager. I have tried 11.10 beta 1 and it has the same problem.  Is there any way to fix this, or at least make it more usable? (I suspect not). Given the recent rise in popularity of netbooks, do you think Ubuntu will include a low-resolution-friendly version in the near future?  How well does KDE deal with these low resolutions? I noticed KDE Plasma has a netbook interface. Is it worth switching for that? I am wondering if the explanations correct and whether what is the difference between different &quot;seems&quot;.   He seems happy. He seems a happy fellow. He seems to be a happy fellow. He seems to work hard. He seemed to be happy   &quot;Seem&quot; also enters into an 'impersonal' construction which employs 1) the 'dummy' subject it + an active tensed form with &quot;seem&quot;, followed by 2) a that clause (sometimes called a 'content' clause) which expresses the assertion which is hedged or qualified.   It seems that he is happy (but he may not be).  It seemed that he was a happy fellow (but he wasn't).  It will seem that he is working hard (but he will in fact be spending his time answering questions on ELL instead of working).  He is seemed to be something. Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$ Prove that the set of rational numbers $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$. I'm unsure about how to prove this. I'm also unsure about the difference between a σ-algebra and a Borel σ-algebra. I have 3 old 3.5" internal hard drives sitting gathering dust at the moment. 2 are SATA, and one IDE. I want to either start putting them to use, or dispose of them to clear up some space.  What is the best approach towards disposing of the drives in terms of thoroughly cleaning the contents before throwing away or selling? Are there any recommendations for good software to use to do this?   Are there any 100% successful methods which result in having a usable drive at the end? Why define an anonymous function and pass it jQuery as the argument? For QA workstations preparation (Windows-based PCs) our IT department uses typical batch deployment tools. I'm not at all interested in the details of such process, but IT guys ask me:  What typical set of software you need for everyday manual testing tasks? We could include these in our deployment so that you guys could save more time for testing, not for environment prep &amp; tuning.  Sure thing we do test various range of projects, from web applications to standalone solutions, and each application requires its own set of tools for manual testing, e.g.:  Browsers Virtualization utilities DB clients Screens capturing tools FTP clients XML editors etc.  However, and that's for sure - there's a list of tools every QA MUST have installed on its PC, regardless of project types under testing. My area of experience is mostly standalone / complex web apps, that's why my vision on the task is a bit subjective. So, your suggestions of what are tools / software an average QA specialist can't live without will be highly appreciated. 2 assumptions:  Manual testing is a point of interest. Let's limit the list to not more than 15 (better 10) items.  Thanks in advance!