Bonjour.  Show that  $$\sum{\frac{1}{n^{2+\cos{n}}}}$$ is a divergent serie. $$\\$$  My main problem is: If $\epsilon$ is “infinitely small positive real number” define $A_{\epsilon}$ as the set of all $n, |2+\cos n|\leq 1+\epsilon$ $(n \in A_{\epsilon}\iff-1\leq \cos n \leq -1+\epsilon)$. The divergence should come from the sum over $A_{\epsilon}$ but I have no idea to how to handle this. $$\\$$
$$ \sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$$  Does it converge or diverge?   Can we have a rigorous proof that is not probabilistic?   For reference, this question is supposedly a mix of real analysis and calculus.
Panasonic Eneloop BK-3MCC (4th gen) - where I can find maximum discharge current? Im looking for some official information source about maximum current for Panasonic Eneloop BK-3MCC rechargeable batteries.  All I found is , there is just 1 table (nothing about maximum discharge current), charge and discharge characteristics.  UPDATE LINK:   / edited - I fixed my mistake, I meant 6A not 8A /  There is discharge characteristic for 6000mA discharge. So... I can safely draw 6A from that AA cell? I posted a question and a couple of respondents asked for the source code. I could only post portions of the code.  If attachments were allowed I could have uploaded a .zip file with the whole application.  Will this be a feature in SO? Let, $D=\{z\in \mathbb C:|z|&lt;1\}$. Which are correct?   there exists a holomorphic function $f:D \to D$ with $f(0)=0$ &amp; $f'(0)=2$. there exists a holomorphic function $f:D \to D$ with $f\left(\dfrac{3}{4}\right)=\dfrac{3}{4}$ &amp; $f'\left(\dfrac{2}{3}\right)=\dfrac{3}{4}$. there exists a holomorphic function $f:D \to D$ with $f\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}$ &amp; $f'\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}$ there exists a holomorphic function $f:D \to D$ with $f\left(\dfrac{1}{2}\right)=-\dfrac{1}{2}$ &amp; $f'\left(\dfrac{1}{4}\right)=1$.   With the help of Schwarz lemma &amp; its applications, we find that $(1)$ is false &amp; $(3)$ is true.  But, I can not think about options $(2)$ &amp; $(4)$. "Any" followed by singular or plural countable nouns? This question has troubled me for ages despite my several attempts of looking it up in dictionaries or usage books. Do we say, "Do you have any ideas" or "Do you have any idea"? I do see an example where "any" means "it doesn't matter who/which/what", therefore "You can borrow any book you like." Also, does it matter between using it in questions and negatives? How to fix invisible form fields in Firefox while using Adwaita Dark Theme (or any other dark theme) I have this issue with some form fields in Firefox and using the adwaita-dark theme. In some webpages where the field background is white, you cannot read the text because it is also white.   This question was edited in order to clarify that this kind of wording of the question might help people who are not familiar with what a GTK+ theme. I also thing that the wording will help to get more hits through search engines. If it's still considered a duplicate, I'll accept it. No connection could be made because the target machine actively refused it (PHP / WAMP) For three days straight, I have connected to the public WiFi network at my local library. Each day, I have seen a different prompt in Terminal. Here are some of the prompts I've seen:  zp-pc:~ russell$ mary-pc:~ russell$ normob05:~ russell$   I have check under System Preferences -> Sharing, and my computer name is "Russell's Mac". Also, I set the DHCP Client ID to "RUSSMAC" under System Preferences -> Network -> Advanced -> TCP/IP, but I still see the random host names at the Terminal prompt.  Why is my computer name changing every day? Is there an easy way to get to www.stackexchange.com from any of the SE sites? One thing I've noticed about the relatively new sitewide layout is that I can't find a quick way to get back to www.stackexchange.com without finding StackExchange in the sites list. As a result, I am typing stackexchange in my toolbar a whole lot more often now. In particular, I tend to enjoy browsing the hot questions list and my own personal feed quite often so visit these pages on a daily basis. Is there an easy link to them that I'm missing?  (On the android app, there is a feed in the menu that I really appreciate, something like that on the desktop would be ideal!) Can the "Sacrifice (this card):" activated ability be placed back on the stack? This is a broad question so for simplicity I will use  and .  Scenario 1: Common exchange- creating a baseline.   Player A uses Naturalize on Seal of Fire  Player B Sacrifices SoF in response. SoF is highest on the stack and goes off first.  This leaves Naturalize without a valid target.   Scenario 2: Complicated exchange- Is this legal?   Player B Sacrifices SoF. In response Player A targets it with Naturalize. SoF is on the stack and it's ability has not resolved. Player B (as above) sacrifices SoF in response to the Naturalize.    Can Seal of Fire be placed back on the stack by re-activating its ability, potentially with a new target? Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra Can't kill a sleeping process java.lang.IllegalArgumentException: Invalid  in servlet mapping &lt;servlet&gt;     &lt;servlet-name&gt;myservlet&lt;/servlet-name&gt;     &lt;servlet-class&gt;workflow.WDispatcher&lt;/servlet-class&gt;     &lt;load-on-startup&gt;2&lt;/load-on-startup&gt; &lt;/servlet&gt;  &lt;servlet-mapping&gt;     &lt;servlet-name&gt;myservlet&lt;/servlet-name&gt;     &lt;url-pattern&gt;*NEXTEVENT*&lt;/url-pattern&gt; &lt;/servlet-mapping&gt;   Above is the snippet from Tomcat's web.xml. The URL pattern *NEXTEVENT* on start up throws     java.lang.IllegalArgumentException: Invalid &lt;url-pattern> in servlet mapping   It will be greatly appreciated if someone can hint at the error. ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ How Do I get into the castle walls? Add max value to a new column in R Spider Identification Illinois I noticed a really huge, beautiful web on my porch last week, and tonight, I discovered its resident. I'm thinking it's an Araneus diadematus (Cross Orbweaver), but I was hoping for some confirmation.   Can anyone confirm this or offer a better suggestion? I am trying to invite my son (IOS Pocket Edition) to my realms server (mac osx).   I keep getting the response "Could Not Invite The Provided Name" when I try to invite him. His name is all regular characters with no spaces . . . just letters and numbers.  Are the two game types incompatible, and if they are Is it possible to create the same type of 24/7 available server that is only open to him and other invitees like the OSX realms?   Thanks in advance for any clarification. Weird behavior when overriding gnome alert styling? After playing around with the i3 tiling window manager, I had my fill and decided to uninstall it and continue using gnome. However, to my dismay, something in i3 overrode the default gnome alert box. For example, when connecting to wifi, I get a gray or blue box instead of the nice ubuntu popups. The screenshot says it all. Any ideas?    (See top right corner) Full List of inventory items After beating the game, I still have several empty inventory spots.  I most likely missed several items in my addicted frenzy to finish the game.  What are all the items that can be found in the game? And where can they found? When I run this command :  apt install libkf5*   I get the following error :  Unable to locate package libkf5*    I'm sure that the packages whose names start with libkf5 exist (tab-completion says so) . So the problem is not about the absence of those packages.(Note the asterisk at the end of that error message , the wildcard's not working at all) I use apt v.1.9. Thanks in advance. How do I prevent widow/orphan lines? How do I prevent a line from appearing by itself:  Orphan: at the bottom of the page, or Widow: at the top of the page?