Radius of convergence of the series $\displaystyle\sum_{n=0}^{\infty}n!z^{2n+1}$
Compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$
How to tell what length of chain to get? What does "href" stand for in HTML? I'm a software developer and as such I build and run programs hundreds of times per day. I've noticed that since I started using Catalina, after compiling and linking there is a delay (which can be seconds) when the internet is slow or having problems (I have bad internet often). If I disable wifi and rebuild, the delay goes away. How can I disable this so my builds run faster? Mafia 3 no more damage to be dealt barclay mills Should I submit bank statements when applying for a UK Visa? What do they say about me? The UK Visas and Immigration Directorate publishes  that provides helpful tips that can result in successful visa applications. Section 2 of this guidance opens is entitled &quot;other documents you may want to provide&quot; (emphasis mine).  Section 2: other documents you may want to provide – all visitors This section provides guidance on the types of documents that you may want to provide to help us consider your application against the Immigration Rules. Previous travel documents/passports, which show previous travel. Financial documents showing that you have sufficient funds available.  These must clearly show that you have access to the funds, such as:  bank statements building society book proof of earnings such as a letter from employer confirming employment details (start date of employment, salary, role, company contact details) where a third party (who is either in the UK or will be legally in the UK at the time of your visit) is providing financial support to you e.g. a business, a friend or a relative, documents to show that they have sufficient resources to support you in addition to themselves and any dependant family should be provided   The first item is &quot;bank statements&quot; and this ties in with the , which says...  evidence that you can support yourself during your trip, eg bank statements or payslips from the last 6 months  (Note 'eg' is a Latin abbreviation meaning &quot;for example&quot;; this appears to be optional rather than a fixed requirement.) Question: How should someone interpret this such that the chances of success are maximized? How many statements should I submit? What are they looking for and what do my bank statements tell about me? My stance is that these websites are a great boon to the research community and they were certainly extremely helpful for my research. I think they should be applauded rather than persecuted, and while they may be illegal now, I think a way to make them legal should be found (in the same way I can download articles legally through my university's subscription to all the major publishers and journals).  Can I thank them in the acknowledgements section of my thesis? Alignment of the titles in a ToC and \Roman{section} There is a problem with the alignment of the numbering of the ToC: When we use   \renewcommand{\thesection}{\Roman{section}}   the numbers encroach on the titles. When the command is commented out, the numbers are all aligned [from the first number on the left] but the titles do not begin at the same position.  What I want is to use \Roman{section} but with the numbers being displaced after V (or 9 in arabic) so that the first letters of the  titles are all aligned !  An illustration:  %\RequirePackage{fix-cm} \documentclass[a4paper, 11pt, twoside]{article}  \renewcommand{\thesection}{\Roman{section}}  \begin{document}   \tableofcontents \normalfont %\cleardoublepage  \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY}  \end{document} How to graphically represent a language I've noticed this on occasion with a variety of applications. I've often thought it was because the output was cancelled early (ctrl+c, for example) or something similar, and zsh is filling in a new line character. But now curiosity has gotten the best of me, since it doesn't seem to do this in bash.   zsh    bash    The Sequence program is something I pulled from a book while reading on Java certifications and just wanted to see if it would compile and run. I did notice that it does not use the println() method from the System.out package/class. Instead it uses plain old print().  Is the lack of a new line character the reason I get this symbol? INI file parsing in PowerShell New messages flagged blue bubble does not go away When someone flags a message in chat all 10k+ users in chat get a little blue bubble to vote on. It shows up in the upper left hand corner of your gravatar (which is in the bottom left of the page).  When someone flags a message and it shows up, if I wait for a second to click on it, and then click on it, and it has already been handled, it shows the message  "There are no flags to display."  In the past, after showing this message, the blue (1) would disappear. However, lately it has not been going away and requires a page refresh in order to remove. Can this be fixed?  This issue is addressed here:  from September 12th 2012. But since it is still occurring 10 months later, I believe the cause is different. How do I check if an element is really visible with JavaScript? In JavaScript, how would you check if an element is actually visible?  I don't just mean checking the visibility and display attributes. I mean, checking that the element is not   visibility: hidden or display: none underneath another element scrolled off the edge of the screen   For technical reasons I can't include any scripts. I can however use  as it is on the page already. How can I get a brace on the right, not the left, to group cases, using cases? (I know actual cases look better with the brace on the left, but the items I need to group are not literally cases. They are a set of steps in an algorithm which I want to consider as an item.)  The following puts the brace on the left. All I need to do is to flip it to the right.  \begin{align} \begin{cases} a&amp;=bbb\\ c&amp;=ddddddd\\ e&amp;=ffffffffff \end{cases} \end{align}   Thanks for any help with this! Does the series $\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}$ converge or diverge? I have this series given by $$\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}.$$ I know that the terms are all nonnegative. Can I get a subsequence of $\frac{1}{n^3 \sin^2n}$ such that its sum diverges to $+\infty$? How to load image to android and resize I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it? Cancel misclicked flags The question is if you have a situation where one of the singular values is equal to 0 in a singular value decomposition of a matrix, how to do you procede to find the column vector of U corresponding to this singular value?   Usually I found the columns of U with this relation, so let's say that we refer to $\vec{u_2}$ as the U column vector corresponding to singular value equal to 0:  $\vec{u_2} = (1/s_2)Av_2$  Now the as we can see the 0 is in an illegal place, since you can't divide by zero. But if you move it to the left side, I still can't quite see how to find the column of U corresponding to it. Any suggestions?  Here is an example of a matrix that provided this specific challenge  $ A = \left(\begin{array}{rrr} -3 &amp; 1 \\ 6 &amp; -2 \\ 6 &amp; -2 \end{array}\right). $  $ \lambda{_1} = 90$,  $\lambda{_2} = 0$,  $s_1 = 3 \sqrt{10}$,  $s_2 = 0$,  How can one find $\vec{v_2}$ when $\lambda{_2} = 0$? In this case, you know that the eigenvectors of $A^{t} A$ are orthogonal, solve for $\lambda{_2}$ and find the eigenvector if it's orthogonal to the eigenvector corresponding to the first eigenvalue you have your solution.  So we end up with the following normalized column vectors for V, which we can see are orthogonal:  $ \vec{v_1} = \left(\begin{array}{rrr} -3/\sqrt{10} \\ 1/\sqrt{10} \\ \end{array}\right). $  $ \vec{v_2} = \left(\begin{array}{rrr} 1/\sqrt{10} \\ 3/\sqrt{10} \\ \end{array}\right). $ White screen of death: Fatal error: Allowed memory size of X bytes exhausted I have a issue with my Drupal installation, for example:   when I enable or disable the modules, It redirects me to a blank page, when I create a new content type and save it, redirects me to a blank page, when I add a new view and save it, it redirects me to a blank page, when I try to clear the cache, it redirects me back to a blank page, or in similar cases.   Basically all the confirmation pages redirect me to a white screen. When I refresh it again, it shows me the page. I tried to increase the PHP memory value but it doesn't help.  Are there any other solutions for this?  The error which I'm having:      Fatal error: Allowed memory size of 100663296 bytes exhausted (tried to allocate 8192 bytes) in sites/all/modules/views/plugins/views_plugin_localization_none.inc on line 1 What does the author mean by 'back to back' and 'hidden city' ticketing hacks? At this link about   what does the author mean by this?   Back to back and hidden city ticketing. Sometimes airlines will charge far more for tickets to that do not include a Saturday night stay, on the assumption that those passengers are business travelers who aren’t flexible and can afford to pay more. Yet those who commute between cities eventually realize that they can purchase one round-trip ticket that covers their first outbound and last return, followed by round-trip tickets to return home on the weekends.