Convergence of $\sum\limits_{n=2}^{\infty}\frac{(n^3+1)^\frac13-n}{\log n}$
Show that the series $\sum\limits_{n=2}^{\infty} \frac {(n^3+1)^{1/3}-n}{\log n}$ converges
How can I capture KeyDown event on a WPF Page or UserControl object? I have a Page with a UserControl on it.  If the user presses Esc while anywhere on Page I want to handle.  I thought this would be as easy as hooking up the PreviewKeyDown event, testing for the Esc key, and then handling it.  However, when I placed I breakpoint in the event handler I found it was never getting called.  I thought perhaps the UserControl might be getting hit, so I tried PreviewKeyDown there... same result.  Does anyone know the proper place to test for a KeyDown or PreviewKeyDown on a Page object? Let us say I have added a PPA that has X package that I want but it also has Y package that I do not want to use or receive updates from. How can I, from the same PPA, receive updates for a specific package but deny updates from the same PPA for other packages.  A step by step example would be good since this has happened to me in several PPAs that have a particular package I want but also add a whole bunch of others that I do not yet want to update. How long does it take for DNS records to propagate? I try to understand and visualize myself covariance matrix. Supposing I have a matrix A = [ 2 3 4; 5 5 6 ], how do I calculate its covariance matrix, and what is its practical meaning? (All I was able to understand by now is that on the diagonal of the covariance matrix, variances for particular variables are placed, and on the upper and lower fields correlations between those variables.) Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$ It is straightforward to show $$\int_{-\infty}^{\infty}\Phi(a+bx) \phi( x ) dx = \Phi\left(\frac{a}{\sqrt{1+b^2}}\right)$$ but what value does $$\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$$ have for $c&lt;\infty$, e.g., for $c=0$? Even a good approximation would really help me! ERROR: cuvid requested, but not all dependencies are satisfied: cuda/ffnvcodec I am trying to compile FFMPEG with Nvidia Cuda support, on Debian 9.3. Parameters, what I am using:  --enable-cuda --enable-cuvid --enable-nvenc --extra-cflags=-I/usr/local/cuda/include --extra-ldflags=-L/usr/local/cuda/lib64 --enable-gpl --enable-libx264 --disable-x86asm --enable-libx265 --enable-libfdk-aac --enable-nonfree   Nvidia Cuda with drivers are installed. When I try to configure ffmpeg, it says:  ERROR: cuvid requested, but not all dependencies are satisfied: cuda   Newer ffmpeg will show a similar, re-worded message:  ERROR: cuda requested, but not all dependencies are satisfied: ffnvcodec   I absolutely don't know why I'm having this issue, because I am compiling ffmpeg on all of our trans-coding servers. Using the properties panel I can add, with "+"  button, only eight UV maps. Is it possible to have more than 8 of them? Converting string into datetime Getting the class name of an instance? Google spreadsheet sorting messes up cell comments I'm running into this weird problem with Google spreadsheets: if the cells have comments on them and I sort the spreadsheet, the rows sort but the comments stay in the same position, and don't move with the cells they're attached to.  In other words, the cells look like this:  A C  &lt;-- comment on this cell B   and then I sort by this column:  A B  &lt;-- comment remains on this cell (stays in position) C  &lt;-- comment should have remained attached to this cell   This means that sorting is completely broken and I can't use it at all, because I clearly need the cell comments to stay with the cell they're attached to.  Is this a bad bug in Google Spreadsheets, or am I missing something here? Email from IOS with attachments larger than 7.5Mb gets stuck in outbox and constantly tries to resend. Costs us hundreds in data fees In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template &lt;typename T, typename Tail&gt; // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template&lt;typename U&gt; struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion&lt;U&gt; dummy;      };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; }; template &lt;typename T&gt; // For the last node Tn. struct UnionNode&lt;T, void&gt; {     // ...     template&lt;typename U&gt; struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; };   The problem I have is in the typedef Tail::inUnion&lt;U&gt; dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion&lt;U&gt; names a type and not a function? Maclaurin series of $\ln(1-x+x^2)$ Is there a closed form expression for $\text{n}^{\text{th}}$ coefficient of Maclaurin series of  $$\ln(1-x+x^2)$$ Is there a route that would allow travel to the US from the UK or Schengen area, given the US travel ban? I'm a European citizen living in the US on a work visa. Due to some unfortunate circumstances, I need to urgently visit my home country. However I would like to get back to the US after my visit is complete. Flying from the US to Europe is not a problem as there are still daily flights between some city pairs. However going back could be tricky, as  anyone who has been in the Schengen area in the past 14 days from re-entering the country.   Is there a flight route that would let me from Europe to some country, stay there for 14 days and then fly to the US? Canada is out, as they've banned international visitors. Mexico seems to keep their border open, but I  any direct European flights from their airports. Almost every other country either suspended flights or doesn't allow foreign nationals to enter. Why can in-class initializers only use = or {}? Calculation of $\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$ Calculation of  $\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$  $\bf{My\; Solution::}$  Let $y=\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$, Now taking $\log_{e}$ on both side  $\displaystyle \log_{e}(y) = \lim_{n\to \infty}\log_{e}\left(\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}\right)=\lim_{n\to \infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right)$  Now Using Reinman Sum of Integral ...  $\displaystyle \log_{e}(y) = \lim_{n\to\infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right) = \int_{0}^{1}\ln(1+x)dx = \log_{e}(4)-\log_{e}(e) = \log_{e}\left(\frac{4}{e}\right)$  So $\displaystyle y =\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}} =\frac{4}{e}$  But how can i solve above question using Stirling Approximation,  May I ask for help?  Thank you in advance! Is there a regular expression to detect a valid regular expression? Is it possible to detect a valid regular expression with another regular expression?  If so please give example code below. Why does Ubuntu create a file ending in ~ for every file I create with a text editor like GNU Emacs? IPv4 vs IPv6 priority in Windows 7 I have IPv6 connectivity through Hurricane Electric tunnel. Since IPv6 day this year, many services (google.com, facebook.com, etc.) enabled IPv6 on their main domains. On my Windows machine, IPv6 is preferred over IPv4. This means that whenever I visit Google, all traffic goes through my tunnel to Hurricane Electric, which raises the latency by more than 100%:  C:\&gt; ping www.google.com  Pinging www.l.google.com [2001:4860:8005::68] with 32 bytes of data: Reply from 2001:4860:8005::68: time=85ms Reply from 2001:4860:8005::68: time=84ms Reply from 2001:4860:8005::68: time=112ms Reply from 2001:4860:8005::68: time=86ms  Ping statistics for 2001:4860:8005::68:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 84ms, Maximum = 112ms, Average = 91ms   C:\&gt; ping -4 www.google.com  Pinging www.l.google.com [173.194.79.103] with 32 bytes of data: Reply from 173.194.79.103: bytes=32 time=28ms TTL=48 Reply from 173.194.79.103: bytes=32 time=28ms TTL=48 Reply from 173.194.79.103: bytes=32 time=55ms TTL=46 Reply from 173.194.79.103: bytes=32 time=29ms TTL=46  Ping statistics for 173.194.79.103:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 28ms, Maximum = 55ms, Average = 35ms   Question: How can I make Windows 7 to always prefer IPv4, when both IPv4 and IPv6 records are available for a specific domain name?