Consider the series  $$\sum_{n=2}^{\infty} \frac{1}{(\log 1)^p+(\log 2)^p+\cdots +(\log n)^p}$$  where $p&gt;0$.  For what $p$, the series converges?  This question appears in the Tier 1 Analysis exam (2014/08) of Indiana University Bloomington. And I modify it a little to make it look more tight...
Suppose $\displaystyle a_n=\frac{1}{(\text{log}2)^p+(\text{log3})^p+...+(\text{log}n)^p}$ for $n\geq 2$ and $p&gt;0$. For which values of $p$ does $\sum_{n=2}^\infty a_n$ converge?  So, when $p\leq 1$, $\displaystyle a_n\geq \frac{1}{(n-1)(\text{log}n)^p}$ for $n\geq 2$. Let $\displaystyle b_n=\frac{1}{(n-1)(\text{log}n)^p}$. Then $\sum b_n$ diverges since $p\leq 1$. Therefore by comparison test $\sum a_n$ diverges when $p\leq 1$.  When $p&gt;1$, $\displaystyle a_n\leq \frac{1}{(\text{log}n)^p}$. Let $\displaystyle c_n= \frac{1}{(\text{log}n)^p}$. If $\sum c_n$ converges then I will win. But now I am stuck. Is $\sum c_n$ converges? Then how can I prove it? If not how can I conclude the state of convergence of $\sum a_n$ for $p&gt;1$?   Can anybody please help?
Which serial protocol or encoding scheme does this scoreboard use? I am trying to decode a signal stream coming from a Nevco scoreboard controller:    Packets like this are sent every ~2.7 ms.  I suspect it is some sort of UART signal because it is on the RX line of a ATMEGA48, but I cannot identify the finer protocol details like parity and stop bits. All the combinations I have tried returns junk data, so it may be another encoding scheme.  What's unusual is that the same signal is also sent to the MOSI pin of the microcontroller, but there is no clock signal anywhere.  A .vcd file is .   The shortest pulses (both high and low) are always 8us in length.    This is what two packets look like. Anyone got ideas? I'm trying to find $\int x^x \, dx$, but the only thing I know how to do is this:  Let $u=x^x$.  $$\begin{align} \int x^x \, dx&amp;=\int u \, du\\[6pt] &amp;=\frac{u^2}{2}\\[6pt] &amp;=\dfrac{\left(x^x\right)^2}{2}\\[6pt] &amp;=\frac{x^{2x}}{2} \end{align}$$  But it's certain that this isn't the correct way to evaluate that, and the answer must be wrong. Limit $\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$ How can I find the following limit :$$\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\left(1-\frac{1}{10}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$$There are four options $(a)\frac1{3}(b)\frac1{9}(c)\frac1{81}(d)0$ Thanks! I have been playing for almost 2 days, and today it is asking me to sign up again.  I have all my game saved in my google account, but I wonder if I just log in from a trainer account will I keep my progress? When does Ubuntu 16.04 use /etc/apache2/ssl/apache.crt? I have some Ubuntu 16.04 server running and set up one vhost in apache2 which uses (or should use) ssl.  &lt;IfModule mod_ssl.c&gt;         &lt;VirtualHost *:443&gt;          ServerAdmin myemail@mailhoster.xx         ServerName my.domain.name.de         DocumentRoot /var/www/mysslsite          &lt;Directory /var/www/mysslsite&gt;                 Options FollowSymLinks MultiViews                 AllowOverride All                 Order allow,deny                 allow from all         &lt;/Directory&gt;          ErrorLog ${APACHE_LOG_DIR}/mysite.ssl.error.log         CustomLog ${APACHE_LOG_DIR}/mysite.ssl.access.log combined          &lt;/VirtualHost&gt; &lt;/IfModule&gt;   I did NOT enable the standard sites-available/default-ssl.conf.  I am able now to browse to  and it is asking in firefox to add some exception which is totally normal if i did not buy any certificate.  But I was wondering where it is set up that it should use the certificates in /etc/apache2/ssl/ directory. I can not find any config where it is told to use that. I all the time was thinking that it will use something from /etc/ssl folder.   Or did I maybe not activate SSL correctly? CKEditor buttons not showing I'm using Drupal CKEditor module 7.x-1.13 and CKEditor 4.3.2. Everything is installed and appears to work fine... except that there are some buttons that don't appear despite being configured to do so, notably "Select All" and the justify left/right/centre/justified buttons. Here are the buttons as configured:    And here are the buttons as they appear: I'm looking for a high current DC switch (able to switch something like 5V@30A) and I've encountered several DPDT that might do what I need, however they are only rated for AC applications (3A@250VAC or 6A@125VAC). Are these rating convertible to DC? or is that something that only the facturarer would know? Compute the mean of $(1 + X)^{-1}$ where $X$ is Poisson$(\lambda)$ Question  Let $X$ be Poisson with parameter $\lambda$.  Compute the mean of $(1 + X)^{-1}$. (Introduction to Probability Theory, Hoel, pp. 104)  Answer Key  The answer key shows that the mean is $\lambda^{-1}(1 - e^{-\lambda})$  My Solution  $$E(1 + X)^{-1} = \sum\limits_{j = 1}^\infty (1 + j)^{-1} \dfrac{\lambda^{(1 + j)^{-1}}e^{-\lambda}}{(1 + j)^{-1}!}$$ $$= e^{-\lambda} \sum\limits_{j = 1}^\infty \dfrac{\lambda^{(1 + j)^{-1}}}{((1 + j)^{-1} - 1)!}$$ $$= \lambda^{-1} e^{-\lambda} \sum\limits_{j = 1}^\infty \dfrac{\lambda^{(1 + j)^{-1} - 1}}{((1 + j)^{-1} - 1)!}$$ $$= \lambda^{-1} e^{-\lambda}(e^{\lambda} - 1)$$ $$= \lambda^{-1}(1 - e^{-\lambda})$$  EDIT: I found why I got the answer incorrect.  Thanks for those who answer the question! :) I need to host several Apache virtual hosts with SSL from a single IP.  Now - I understand that because SSL wraps around the HTTP request, there's no way to know which host is being requested until a public key has been sent to the client first. This essentially breaks the possibility of SSL virtual hosts using a standard SSL certificate.  I have obtained a Unified Communications Certificate (UCC), otherwise known as a Subject Alternative Name (SAN) certificate. This allows me to serve the same certificate for multiple domains.  I would like this to be the certificate served by Apache for any SSL request - and then have Apache resolve the virtual host as usual, once the encryption has been established.  How should I configure Apache for this? I have tried to research how this can be done, but all I can find are quotes which say that it is possible, but no specifics:    wiki.apache.org/httpd/NameBasedSSLVHostsWithSNI     While Apache can renegotiate the SSL   connection later after seeing the   hostname in the request (and does),   that's too late to pick the right   server certificate to use to match the   request hostname during the initial   handshake, resulting in browser   warnings/errors about certificates   having the wrong hostname in them.   serverfault.com/questions/48334/apache-virtual-hosts-with-ssl     Incidentally, it is possible to have   multiple SSL-secured named virtual   hosts on a single IP address - I do it   on my website - but it produces all   sorts of warnings in the Apache logs,   and certificate warnings in the   browser. I certainly wouldn't   recommend it for a production site   that needs to look clean.   -David Jul 31 at 4:58   www.digicert.com/subject-alternative-name.htm     Virtual Host Multiple SSL sites on a single   IP address. Hosting multiple   SSL-enabled sites on a single server   typically requires a unique IP address   per site, but a certificate with   Subject Alternative Names can solve   this problem. Microsoft IIS 6 and   Apache are both able to Virtual Host   HTTPS sites using Unified   Communications SSL, also known as SAN   certificates.     Please help. Nearby objects won't move independently? Enroll Apple Developer Program under 18 I've seen a lot of questions like this throughout the web but they're mostly from 2 or 3 years ago, so I decided to ask to have some updated answers.   I'm 16 and I want to start publishing and using the benefits that comes with the Developer Program. In the legal agreement says that I should be over 18, and I'm not so, i can't do it. I've contacted the apple developer support and they told me that I should use a account in my father's name. We reside in Brazil. With that, I had some doubts:   Will the name on the App Store be mine or my father's? In the future, when I'm 18, this account can be transferred to my name?   Besides that, if someone has any advice or (legal) workaround I'd appreciate it, thanks I have some long URLs which doesn't contain special "line break characters" like "-" or "/". How can I automatically break these URLs?  \documentclass{scrreprt}  \usepackage[ngerman]{babel}                     \usepackage[latin1]{inputenc}                 \usepackage[T1]{fontenc} \usepackage[backend=biber]{biblatex} \usepackage{url} \usepackage{dingbat}  % for \carriagereturn symbol \makeatletter \g@addto@macro{\UrlBreaks}{\UrlOrds} \g@addto@macro{\UrlBreaks}{% \do\/\do\d% } \makeatother  \begin{filecontents}{bachelorarbeit_lit.bib} @ONLINE{java96,     author = {{Joe Black}},     title = {Foobar 1.0},     year = {1996},     month = {1},     url = {http://www.aaa.bb.cccc.dh/uploads/dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd.pdf},     urldate = {2011-03-02},     sortname = {Sun},     keywords = {www} } \end{filecontents}  \bibliography{bachelorarbeit_lit}  \begin{document} Test \cite{java96} \printbibliography \end{document}   edit  I don't know why but it still doesn't work. Is there an option to automatically break long URLs. I don't care where the break is but it should be done automatically. Even if I manually specify the "breaking character" it doesn't work (as the example shows). How to evaluate the integral $$\int_{25\pi / 4}^{53\pi / 4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx\ ?$$ How do I install a .tar.gz (or .tar.bz2) file? My new laptop came preinstalled with Windows 8. Naively, as I am, I just formatted the harddrive and installed fine old Ubuntu. Now I want to install Windows 8 for dual boot again, but I have no DVD and do download the ISO one needs a product key. That key is not on the back of the laptop anymore but somewhere on the mainboard.  Is there any way to recover the product key from the mainboard using Ubuntu? Google Chrome is not starting I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated Conditionally Rendering Visualforce element based on user profile I have a controller extension and want to use the Tabbed view to get rid of the Chatter caused endless scrolling.      public class UserProfileGetter {     public UserProfileGetter(ApexPages.StandardController controller) {      String userProfileName = [select u.Profile.Name, id, UserType from User u where u.id = :Userinfo.getUserId()].Profile.Name;      system.debug('Profile===================='+userProfileName);      }    }   When I run the debug it shows my Profile as 'System Administrator' correctly.  My VF page code:  &lt;apex:page standardController="Account" extensions="UserProfileGetter" showHeader="true" tabStyle="account" &gt;   &lt;apex:tab label="Opportunities" name="Opportunities" id="tabOpp" rendered="{userProfileName!='Chatter Content'}"&gt;          &lt;apex:relatedList subject="{!account}" list="opportunities" /&gt;       &lt;/apex:tab&gt;        &lt;/apex:tabPanel&gt; &lt;/apex:page&gt;   So the logic for render I want is - if the user profile name isn't Chatter Content, render. But if I have this logic in the page it won't render for anyone, including me. Ideas? Thanks  Amending - to query other variable on the user, a checkbox called "Admin Team" to display the tab for Account Teams related list, I query for both like this:  public class UserProfileGetter {     public String userProfileName {         get {             return [                     select Profile.Name                     from User                     where Id = :Userinfo.getUserId()                     ].Profile.Name;         }     }     public boolean userAdminTeam {         get {             return [                     select Admin_Team__c                     from User                     where Id = :Userinfo.getUserId()                     ].Admin_Team__c;         }     }      public UserProfileGetter(ApexPages.StandardController unused) {     }   }   And then I use like this:   &lt;apex:tab label="Account Team" name="Account Team" id="Act" rendered="{!userAdminTeam}"&gt;   Thanks all. Query is slow in SQL Server 2014, fast in SQL Server 2012 During the migration of one of our databases from SQL Server 2012 (SP1, CU2) to SQL Server 2014 (SP1), we have experienced some strange issues.  One of the queries that completes within seconds on SQL Server 2012 seem to be hanging on SQL Server 2014.  SELECT  DISTINCT      src.[Id] FROM     [stg].[BaseVolumes] src JOIN          [tmp].[Dates] d ON src.[CalWeek_Nmbr] = d.[CalYrWkDense_Nmbr] WHERE        EXISTS (SELECT  *             FROM                     (SELECT     ctry.[ISOCode]                  AS  [Mkt_Code]                             , so.[Code]                     AS  [SlsOrg_Code_AK]                             , so.[DistributionChannelCode]  AS  [DistChnl_Code_AK]                             , prd.[SupplierCode]                AS  [SKU_Code_AK]                             , cl6.[Code]                        AS  [CstHierLvl06_Code_AK]                             , lp.[BaseDateID]                   AS  [Dte_EK]                  FROM   [PM_APP].[edw].[BaseVolumeDayCurrent]   lp                  JOIN   [PM_APP].[dbo].[Country]                ctry    ON  lp.[CountryID] = ctry.[ID]                  JOIN   [PM_APP].[dbo].[SalesOrganisation]      so      ON  lp.[SalesOrganisationID] = so.[ID]                  JOIN   [PM_APP].[dbo].[Product]                prd     ON  lp.[ProductID] = prd.[ID]                     JOIN   [PM_APP].[dbo].[CustomerLevel6]         cl6     ON  lp.[CustomerID] = cl6.[ID]                  WHERE                        lp.[ModifiedByApp] = 1) lkp             WHERE                    src.[Mkt_Code]                  =   lkp.[Mkt_Code]                 AND src.[SlsOrg_Code_AK]        =   lkp.[SlsOrg_Code_AK]                 AND src.[DistChnl_Code_AK]      =   lkp.[DistChnl_Code_AK]                 AND src.[SKU_Code_AK]           =   lkp.[SKU_Code_AK]                 AND src.[CstHierLvl06_Code_AK]  =   lkp.[CstHierLvl06_Code_AK]                 AND d.[Dte_EK]                  =   lkp.[Dte_EK]         )   Row count:   BaseVolumes:            23108  Dates:                  18628  BaseVolumeDayCurrent:   108115503  Country:                249 SalesOrganisation:      29 Product:                18446 CustomerLevel6:         295   Wait stats showing high CXPacket, but there is one hanging task with SOS_SCHEDULER_YIELD, (print from sys.sysprocesses)   spid | blocked | waittime | lastwaittype          | cpu     | physical_io   76   | 0       | 9886044  | CXPACKET              | 13902   | 31192  76   | 0       | 0        | SOS_SCHEDULER_YIELD   | 9829719 | 83077  76   | 0       | 11248    | CXPACKET              | 11110   | 0 . . .   Attached are the execution plans from SQL Server 2012 and SQL Server 2014.       Any help much appreciated. For the Quadratic Form $X^TAX; X\in\mathbb{R}^n, A\in\mathbb{R}^{n \times n}$ (which simplifies to $\Sigma_{i=0}^n\Sigma_{j=0}^nA_{ij}x_ix_j$), I tried to take the derivative wrt. X ($\Delta_X X^TAX$) and ended up with the following:  The $k^{th}$ element of the derivative represented as  $\Delta_{X_k}X^TAX=[\Sigma_{i=1}^n(A_{ik}x_k+A_{ki})x_i] + A_{kk}x_k(1-x_k)$  Does this result look right? Is there an alternative form?  I'm trying to get to the $\mu_0$ of Gaussian Discriminant Analysis by maximizing the log likelihood and I need to take the derivative of a Quadratic form. Either the result I mentioned above is wrong (shouldn't be because I went over my arithmetic several times) or the form I arrived at above is not the terribly useful to my problem (because I'm unable to proceed).  I can give more details about the problem or the steps I put down to arrive at the above result, but I didn't want to clutter to start off. Please let me know if more details are necessary.  Any link to related material is also much appreciated. Let $(X,d)$ be a metric space. How to prove that for any closed $A$ a function $d(x,A)$ is continuous - I know that it is even Lipschitz continuous, but I have a problem with the proof:  $$ |d(x,a) - d(y,a)| \leq d(x,y) $$ for any $a\in A$ - but we cannot just replace it by $|d(x,A) - d(y,A)|\leq d(x,y)$ since the minimum (or infimum in general) can be attained in different points $a\in A$ for $x$ and $y$, so we only have that $$ |d(x,A)-d(y,A)|\leq d(x,y)+\sup\limits_{a,b\in A}d(a,b) $$ which does not mean continuity.