$$\mu = \sum\limits_{k=0}^{\infty}\dfrac{2^{k}}{\displaystyle{2k+1 \choose k}}$$  The answer is $\dfrac{\pi}{2}$. But I don't know how to do it. Please show me the way! Thank you.
How to find the sum of this series?  $$\sum_{k=0}^{\infty}\cfrac{{2}^{k}}{\binom{2k+1}{k}}$$  It seems very easy. But I still can not work it out, can anyone help?
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$ How do I display a decimal value to 2 decimal places? When displaying the value of a decimal currently with .ToString(), it's accurate to like 15 decimal places, and since I'm using it to represent dollars and cents, I only want the output to be 2 decimal places.   Do I use a variation of .ToString() for this? Making separate Python installation that can call ArcPy? I see a lot of Q&amp;As asking how you can create a separate Python installation (e.g. the Anaconda or Python XY distribution) that can use arcpy, while not 'breaking' the original ArcGIS python installation.  I had this same problem, and I think I have found a 'universal' solution. So far we have done this on about 8 computers at work and it all works fine.   How to install a separate Python distribution that can use ArcGIS? Flight cancelled but doesn't show up on status I booked a SpiceJet flight from Dubai to Ahmedabad on Dec 16 (SG-16) scheduled to depart at 7:25 PM. At noon I received an SMS from SpiceJet to advise me that my flight has been delayed by 4h 50m. Sure enough, when I checked flight status on SpiceJet's website, that was the case. But on other websites like flightstats.com and dubaiairports.ae, the status was that flight was "delayed by 2h 25m".    At 5 PM, I got an SMS that flight had been cancelled. I double checked on Spicejet's website and that too showed the flight to be cancelled. But both flightstats.com and dubaiairports.ae still showed the flight as delayed by 2h 25m.    I went to the airport and met SpiceJet officials. Sure enough, the flight was cancelled. But somehow, the flight cancellation status never made it to the system. I have a Tripit Pro account, and even that never sent me an alert for that. I contacted the travel agent through which I booked my flight (makemytrip) for a refund, and they said that their system doesn't show that flight was cancelled. Now, even the Spicejet website has removed the cancellation status from that flight.    Apart from the SMS, I now have no proof that my flight was cancelled.    Can someone tell me, how can I proceed with a refund claim? Alpha over layers but maintain environment background How do I make a 2D game resolution independent? Is there a command like "watch" or "inotifywait" on the Mac? Unzip File: Permission Denied I am trying to unzip a file (Facebook download-your-info zip file), but here's what I got:   Is there a way I can force-unzip it?  Update: I tried sudo unzip file.zip -d destination_folder in terminal, and it unzipped the file, but what came out, all the files have size 0 bytes:   Update 2: I do have permission to the directory and the file.    (I'm really sorry if my question is asked badly. Let me know down in the comments :) ) How do I determine the size of an object in Python? I want to know how to get size of objects like a string, integer, etc. in Python.  Related question:   I am using an XML file which contains size fields that specify the size of value. I must parse this XML and do my coding. When I want to change the value of a particular field, I will check the size field of that value. Here I want to compare whether the new value that I'm gong to enter is of the same size as in XML. I need to check the size of new value. In case of a string I can say its the length. But in case of int, float, etc. I am confused. I'm considering taking a loan on my 401k in order to pay off and close 2 credit cards.  I have approximately 30 years until I consider retiring.  The amount of the loan will be $1700 which is less then 20% of my current 401k balance.  I will continue to put 9% of my paycheck into a Roth 401k, and my employer matches 9%.  The loan will be paid back at 3.25% (to myself) and does have $183 in fees.  There are 2 cards I will pay off and close if I follow through with this plan.  One card is 17.9% interest with roughly a $650 balance.  The other is 23% (ish) with roughly a $1,025 balance.  Both of these cards do have an annual fee associated with them, I used them to rebuild my credit and have a newer, lower interest, no fee card that I will keep active for emergencies.  Would it be advantageous for me to pay off these two credit cards and cancel them with a 401k loan? How to approach the modeling of duct work, piping, wiring? Good color palette, usable for the color blind. I'm designing a chart right now, that will slowly have more items added to it. I'd like to create an list/order of colors for the items, that will be most usable for the color blind to differentiate between each item. Any ideas how/where to start? Delay in 4-bit ripple carry adder? In pic below I have drawn a full adder and mentioned their delays, please help me to verify my answer. Been trying to find graphic novel for decades - at least I think it's a graphic novel I am testing the new  &lt;lightning:datatable&gt;, it is really good, and is a good replacement for most of my use cases which today I use a custom list component that I have developed.  I am getting data from my server through apex method, to populate it into the &lt;lightning:datatable&gt; component. I can bind the returned list directly to the data attribute and if the column names are same as the field names, all data is bound correctly.  The problem occurs when I get data from a parent record. For example - I want the Account name of my contact.  This example can show the problem:  Component Markup    &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}"/&gt;  &lt;aura:attribute name="mydata" type="Object"/&gt; &lt;aura:attribute name="mycolumns" type="List"/&gt; &lt;aura:attribute name="sortedBy" type="String"/&gt; &lt;aura:attribute name="sortedDirection" type="String"/&gt;  &lt;lightning:datatable data="{! v.mydata }"                      columns="{! v.mycolumns }"                      keyField="Id"                      onrowselection="{! c.getSelectedName }"                      onsort="{!c.updateColumnSorting}"                      sortedBy="{!v.sortedBy}"                      sortedDirection="{!v.sortedDirection}"                      hideCheckboxColumn="{!false}" /&gt;        Component Controller  ({     doInit: function (component, event, helper) {         component.set('v.mycolumns', [                     {label: 'Id', fieldName: 'Id', type: 'id', sortable:"true"},                     {label: 'First Name', fieldName: 'FirstName', type: 'text', sortable:"true"},                     {label: 'Last Name', fieldName: 'LastName', type: 'text', sortable:"true"},                     {label: 'First Name Hebrew', fieldName: 'First_name_Hebrew__c', type: 'text', sortable:"true"},                     {label: 'Last Name Hebrew', fieldName: 'Last_name_Hebrew__c', type: 'text', sortable:"true"},                     {label: 'Account', fieldName: 'Account.Name', type: 'text', sortable:"true"},                     {label: 'Email', fieldName: 'Email', type: 'email', sortable:"true"},                     {label: 'Phone', fieldName: 'Phone', type: 'phone', sortable:"true"}                 ]);          var action = component.get("c.getRecordsFromDb");         action.setParams({             sObjectName: "Contact",             commaDelimitedFieldNames: "Id,FirstName,LastName,First_name_Hebrew__c,Last_name_Hebrew__c,Account.Name,Email,Phone",             filter: ""         });         action.setCallback(this, function(response){             var state = response.getState();             if (component.isValid() &amp;&amp; state === "SUCCESS") {                 var data = response.getReturnValue();                  component.set("v.mydata", data);             }         });         $A.enqueueAction(action);     } })   APEX Aura Enabled Method  @AuraEnabled public static List&lt;sObject&gt; getRecordsFromDb(String sObjectName,         String commaDelimitedFieldNames,         String filter) {      system.debug('\n\n\n\ngetRecordsFromDb sObjectName: ' + sObjectName + ', commaDelimitedFieldNames: ' + commaDelimitedFieldNames + ', filter: ' + filter + '\n\n\n\n');      // create a dynamic soql to get the value of the field     String sql = 'SELECT ' + commaDelimitedFieldNames + ' FROM ' + sObjectName;      if (!String.isBlank(filter))         sql += ' WHERE ' + filter;      system.debug('\n\n\n\ngetRecordsFromDb sql: ' + sql + '\n\n\n\n');     List&lt;sObject&gt; records = Database.query(sql);     system.debug('\n\n\n\ngetRecordsFromDb: ' + records + '\n\n\n\n');      return records; }   The problem is with the Account.Name field - the &lt;lightning:datatable&gt; component does not display the column data.   I know that the data is returned ok, and I know that in the object that is returned, the Account is contained like an object (probably this is the problem):    Is there a good way to show parent record data with this component? Is there a max array length limit in C++? Is there a max length for an array in C++?  Is it a C++ limit or does it depend on my machine? Is it tweakable? Does it depend on the type the array is made of?  Can I break that limit somehow or do I have to search for a better way of storing information? And what should be the simplest way?  What I have to do is storing long long int on an array, I'm working in a Linux environment. My question is: what do I have to do if I need to store an array of N long long integers with N > 10 digits?  I need this because I'm writing some cryptographic algorithm (as for example the p-Pollard) for school, and hit this wall of integers and length of arrays representation. I just installed Oracle's Java version 7u7 on my Mac (running OSX Mountain Lion). However, when I run java -version it still displays the old version (6u29).    How do I fix this? Do I even need to fix this? What version will browsers (Firefox) use in this case? And what version will be used when I run Java applications directly?  I've seen  but this doesn't work in my situation (probably because this question is about the JRE and the other question about the JDK). In my case the Java Preferences app only displays Java 6 versions (32 bit and 64 bit).    Update:   which java points to /usr/bin/java /usr/bin/java is a symlink to /System/Library/Frameworks/JavaVM.framework/Versions/Current/Commands/java /System/Library/Frameworks/JavaVM.framework/Versions/ only contains the folder A (awesome version name) - which Current points to. Update Migration Path List for Non-Moderators 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! Permutation with prime order, fixed point Let $M$ be a finite set and $\varphi$ a permutation of this set with prime order $q$. How do I show that $\varphi$ has a fixed point if $q$ is not a divisor of $|M|$?