I try to calculate $\sum_{i=1}^{n-1} i\alpha^{2i}$ I think one week but still have no ideas to this sigma,thank everyone
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!
I use Chrome across 4 different workstations and I have my extensions synced across all of them.  The problem I have is that one of the extensions () works great if you've got an actual mouse, but on a trackpad on Ubuntu, it just gets in the way.  If I disable it on the Ubuntu machine, it gets disabled on all Chrome installations due to its .  Q: Can I selectively disable an extension on just a single machine? I know that I have to use some tweaking tool and then a extension for this. But all extensions that are suggested for this(Workspace grid, Workspace matrix), aren't available in the software center. How do I use the Tooling API to create a new Apex Trigger? How do I use the Tooling API to create a new Apex Trigger (rather than update an existing one)?  According to the  I need to specify the ContentEntityId as an existing Trigger Id. But in my case I don't have an Id because I've trying to create a new sObject.  If I omit the ContentEntityId I get an error back in the SaveResult:     Status Code: INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY   Message: "insufficient access rights on cross-reference id"   The following is more or less a test case in C# that attempts to use the SOAP tooling API to create the new trigger.  SforceService toolingService = //... Get instance of the Tooling API  MetadataContainer container = new MetadataContainer(); container.Name = "Test" + DateTime.Now.Ticks;  SaveResult[] saveResult = toolingService.create(new sObject[] { container }); string metaDataContainerId = saveResult[0].id;  ApexTriggerMember apexTriggerMember = new ApexTriggerMember(); apexTriggerMember.MetadataContainerId = metaDataContainerId; apexTriggerMember.Body = "trigger TestOpportunityBeforeUpdate on Opportunity (before update) {\n//Horray\n}";     // Adding this will successfuly update the existing trigger //apexTriggerMember.ContentEntityId = "01q70000000GuzP";  SaveResult[] triggerSaveResults = toolingService.create(new sObject[] { apexTriggerMember }); Assert.AreEqual(1, triggerSaveResults.Length); SaveResult triggerSaveResult = triggerSaveResults[0]; if (!triggerSaveResult.success) {     Assert.Fail(triggerSaveResult.errors[0].message); } Assert.IsTrue(triggerSaveResult.success);  ContainerAsyncRequest containerRequest = new ContainerAsyncRequest(); containerRequest.MetadataContainerId = metaDataContainerId; containerRequest.IsCheckOnly = false;  SaveResult[] containerResults = toolingService.create(new sObject[] { containerRequest }); Mathematician learning theoretical physics See screenshot:    Curiously, there are older badge achievement messages further down the list which display properly. How to install Ubuntu 18.04 alongside Windows 10 How do you file a bug report for Windows? I have come across an issue that I feel is a  in Windows 7. What is the official process for submitting an issue to Microsoft from a consumers perspective as an end user of Windows? I'm trying to prove that the characteristic of any field $F$ is either $0$ or a prime number, but I have no idea what to do.  Help? I have the following equation, where there is a lot of stuff under the sum symbol:  \begin{equation} d(\vec{x},\vec{y})=   \sum_{Z_{xy}\in\vec{Z}_{xy},\forall x\in\vec{x},\forall y\in\vec{y}}      f(Z_{xy}) \end{equation}   In the resulting document, I find it kind of hard to read. Is there a way to write the equation to make the result more readable, e.g. putting the stuff under the sum symbol on different lines? How do I create an immutable Class? \overline outside of math mode If I want to draw an overline over some text, not an equation, how can I do it? \overline seems to only work in math mode, and when used outside of math mode, it automatically says "Missing $ inserted". I'm seeing red dots everywhere On all Stack Exchange sites where I have review privileges, the review queue menu icon has a red dot. No matter what I try, it doesn't go away.     on Meta Stack Overflow might or might not be related. Trying to identify a story about breaking out of a predefined path and no one notices I vaguely remember reading a short story many years ago where something happens and the protagonist gets a bit "out of step" with the rest of the world.  Everyone else keeps acting as if he's still doing what he would have been doing before the event, to the point of carrying on one-sided conversations and the like.  I can't remember much of the plot, but the premise stuck with me.  Edit: To try and explain it more clearly, based on the comment I just wrote, I think everyone else was effectively acting like they were robots with a prerecorded program.  If someone would normally wake up, drink coffee, put on pants, then walk out the door to catch a bus, then if the protagonist broke his coffee cup, stole his pants, and jammed the door, the victim would pour coffee into a broken/nonexistent cup, walk out pantsless, but when he got to the jammed door he might suddenly realize something was up (and thus being "out of step" spreads) or he might continue to go through the motions.  In either case, no one else would notice that the victim was pantsless (or that he didn't make it to work)...  How much of this actually came up in the story, I don't remember. How to implement draggable tab using Java Swing? How do I implement a draggable tab using Java Swing? Instead of the static JTabbedPane I would like to drag-and-drop a tab to different position to rearrange the tabs.  EDIT: . Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$ Any help would​ be appreciated.  My initial attempts were using Lagrange's Mean Value Theorem first between $f(0)$ and $f(1)$ to show that $f'(t)=1$ for some $t$ in $(0,1)$.  Now applying LMV between $f'(t)$ and $f'(0)$, and $f'(t)$ and $f'(1)$ I could prove it if t lies in either $(0,1/4]$ or in $[3/4,1)$. Don't really know where to go next. A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $ Show that an operation being commutative is a structural property I've been looking for a simple regex for URLs, does anybody have one handy that works well?  I didn't find one with the zend framework validation classes and have seen several implementations. I have done major updates to my website, and renamed all my URLs.  How can I tell Google that I have renamed these URLs and let Google refresh its index?  My website URL: http://www.pndmasr.com/  My sitemap: http://www.pndmasr.com/sitemap.xml  I have uploaded my sitemap via Google Webmaster Tools many times.  However, every time I search Google for "pndmasr", I still get results with old pages. I have waited more than 3 days but the problem remains. Any suggestions?  Is there a problem with my sitemap? Description list with aligned descriptions is exactly what I'm looking for. I want my description environment to produce this:  Label is long   text  lab2            blalballalaa label3          possible second rule label four      hello world   Someone offered this:  \newenvironment{mydescription}[1]                                                   {\begin{list}{}%    {\renewcommand\makelabel[1]{##1:\hfill}%    \settowidth\labelwidth{\makelabel{#1}}%    \setlength\leftmargin{\labelwidth}    \addtolength\leftmargin{\labelsep}}}   {\end{list}}   Which works great (the parameter is the longest label), except I think the enumitem should be able to do this. Unfortunately, the documentation for it is extremely confusing to me. Could someone show me how to achieve the same result with enumitem?