$\sum_{n=1}^{\infty} \frac{i^n}{n}$
$\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
Can I travel after visa's intended travel date? I just finished applying for my visa and had originally planned to travel on the 30th of September, so I put that as my intended date of travel. But now I will not be leaving until close to the second week of October.  How does this work, will I still be able to travel with this visa even though it says I intended to arrive on September 30th? I have functionality on a cloud page that depends on the cloud page url. I know how to Requestparameter(), but how do I get the entire url using ampscript or SSJS? Rules for refreezing food How do I clear Bash's cache of paths to executables? When I execute a program without specifying the full path to the executable, and Bash must search the directories in $PATH to find the binary, it seems that Bash remembers the path in some sort of cache. For example, I installed a build of Subversion from source to /usr/local, then typed svnsync help at the Bash prompt. Bash located the binary /usr/local/bin/svnsync for "svnsync" and executed it. Then when I deleted the installation of Subversion in /usr/local and re-ran svnsync help, Bash responds:  bash: /usr/local/bin/svnsync: No such file or directory   But, when I start a new instance of Bash, it finds and executes /usr/bin/svnsync.  How do I clear the cache of paths to executables? How to fully backup non-rooted devices? I know I'm asking for the close-to-impossible -- as a real full-backup certainly requires root permissions. But still there are many folks around not wanting to root their devices -- afraid of voiding their warranties or bricking their devices, or just not having their devices supported by any rooting method.  I also know there were a lot of questions asked already on this topic, and I checked all of them having the backup tag -- none covers the entire topic, all just have pieces, and especially people new to Android (but other non-power-users as well) would have a hard time figuring out the best way.  So I want a detailed canonical answer to the question:  Not involving root-solutions, how to achieve a backup as close as possible to a full backup?  Please do not give simple one-liner answers like "Use app xyz [full-stop]." If mentioning an app (and I doubt a single app would be the answer here), include what parts are covered by it -- as well as ideas on how to fill the gaps it leaves. (And to make it absolutely clear: I know the first thing coming to mind is Titanium Backup -- I use it myself, but this does not apply here: This question is strictly about methods for non-rooted devices!) Moreover, the answer should be as generic as possible in terms of applying to a wide range of devices (i.e. it should not be restricted to one device or manufacturer).  I already mentioned having investigated all questions here tagged backup. These will certainly be helpful providing details for answers here, so I will list up the topmost ones concerning my question:            All these provide some details for my question (so feel free to get inspired by them) -- but I feel there are still details missing. Also it would be helpful to have a summary -- say, an answer including the full description of "the maximum possible".  A last criterium: While I'd consider cloud-based solutions legit, I'd favour local solutions. If you can provide both: all the better. But some people value privacy quite high (I'm one of them), and thus would not trust their data to some cloud service.    Thanks to Ryan, we now have a solution for a really complete backup of all apps and their data -- which I didn't dare to hope for! The only disadvantage: His solution only works for less than 10% of all Android users; namely those whose devices are running at least with Android 4.x.  So again, I ask the close-to-impossible: Any solutions applicable at least on Gingerbread (2.3.x) or, better, even Froyo (2.2.x) -- so they cover the majority of current devices? These solutions may involve multiple tools (try to keep it as simple as possible though; think of your mother to follow your instructions ;)  And keep in mind: NO ROOT!    To further motivate high-quality answers (and hopefully avoid low-quality ones), I will be a harsh one here: As I rarely do, I will down-vote answers not fitting the mentioned criteria on one end -- but on the other end, I will setup a bounty for the best answer (which cannot be done immediately, but earliest after 2 days). Maximum Likelihood Estimator for $\theta$ when $X_1,\dots, X_n \sim U(-\theta,\theta)$ Exercise :     Calculate a Maximum Likelihood Estimator for the model $X_1,\dots, X_n \; \sim U(-\theta,\theta)$.   Solution :  The distribution function $f(x)$ for the given Uniform model is :  $$f(x) = \begin{cases} 1/2\theta, \; \; -\theta \leq x \leq \theta \\ 0 \quad \; \; , \quad\text{elsewhere} \end{cases}$$  Thus, we can calculate the likelihood function as :  $$L(\theta)=\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n\mathbb I_{[-\theta,\theta]}(x_i)= \bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[0,\theta]}(|x_i|) $$  $$=$$  $$\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(|x_i|)\prod_{i=1}^n \mathbb I_{[0, +\infty]}(|x_i|)$$  $$=$$  $$\boxed{\bigg(\frac{1}{2\theta}\bigg)^n\prod_{i=1}^n \mathbb I_{[-\infty,\theta]}(\max|x_i|)}$$  Question : How does one derive the final expression in the box from the previous one ? I can't seem to comprehend how this is equal to the step before.  Other than that, to find the maximum likelihood estimator you need a $\theta$ sufficiently small but also $\max |x_i| \leq \theta$ which means that the MLE is : $\hat{\theta} = \max |x_i|$. Motor to spin slowly, low torque I use Windows 10 with the same Microsoft account on 3 different computers, each one with a different physical keyboard layout: ITA, UK, DE.  In "Control panel - Clock and International settings - Language" I have ITA as display language with ITA/DE/UK keyboard layouts, followed by ENG(US) with only UK layout.  In the same window I opened "Advanced settings" where I set an override (second drop-down list) to the default ("the first one on the list") language/keyboard: that would be ITA/ITA, while I want (on this computer) ITA/DE.  However, when now I log in in the other computers, I get ITA/DE there as well, while each computer should have a different one, being the physical keyboards different: ITA/DE here, ITA/UK on the second one and ITA/ITA on the third one.  If I change one, they all change. And if I don't apply the override, the issue seems to be the same.  Basically the last used language AND keyboard settings are stored on the cloud and applied wherever I log in.  How to set Windows 10 to remember, PER computer, the last used language/keyboard layout settings, without having that setting follow me? I want to copy/modify/delete a Minecraft world. Where can I find my saves folder? This questions has already been asked a million times, but nothing solved my issue so far.  Situation   I'm using Blender 2.72b.  I'm not using nodes, just the plain old vanilla settings. But apparently I messed them up somehow. I'm using the Mirror modifier. I'm completely new to blender (and 3D modelling in general) and use it for a couple of days now. I deleted the cube and made this model from scratch (no import).   In texture view everything looks fine:   In material view (and after rendering) everything is black:   Attempts to solve   I have a light source. I have a camera. I have no ceiling. I have a material. I have a texture. Shadows are activated. I tried using nodes and my output was well connected - no change, still black, so I stopped using nodes again (I had no idea what I was doing anyway). I checked out many solutions posted on the web.   As my last attempt, I opened the vanilla start-up file again. Everything works fine with the cube. So I compared the material und texture settings step by step. It all seems the same. This topic is so extraordinary complex and I'm so bloody inexperienced that I'm stuck at this point. Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals Let $\{a_n\}$ be an unbounded, strictly increasing sequence of positive real numbers and let $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$. Which of the following statements is/are correct? (CSIR NET December 2014)         For all $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;1-\bf{\frac{a_m}{a_n}}$   There exist $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;\frac{1}{2}$      My attempt:  Analysing question in light of $a_k=k\implies x_k=\frac{k+1-k}{k+1}=\frac1{k+1}$, I feel both are correct, I doubt if  I can generalise the result in light of this one example.   Any way to prove that this true for general case?    Note: Please do not confuse  with my question. The first two options are different, I've marked the difference in bold. How to get rid of update notifications for a given app in Google Play Store? General question I have an app X installed on my device in version Y. I don't want to update it to any newer version (Y+z) for some reason. Still, the Google Play Store app always lists updates for X, which keeps me from a simple &quot;update all&quot;. My question, put to a single sentence:  How to hide updates for X permanently from the &quot;available updates&quot; list?   Specific examples First, I know there are alternatives as e.g. the , which can handle this quite well (skip this update, skip all future updates). I prefer a &quot;generic solution&quot;, which does not depend on a 3rd party's market app. Second, I know that  includes a &quot;Market doctor&quot;, which can be used to disconnect an app from Google Play.1 However, in my specific case that only worked for a few hours: I disconnected GTalk, as I don't want it replaced by Hangouts. The update notification disappeared for a few hours, then it was back. No idea what restored the &quot;link&quot;. Third, just to make sure: I'm not talking about the &quot;auto update&quot; feature as discussed e.g. in . I was rather hoping for something close to , but without the need to &quot;freeze&quot; the app in question (which I still want to use, but in the version installed, not in a &quot;future version&quot; available). Fourth: No, uninstalling the app in question is no option here, though it would perfectly hide any future updates from being displayed :) Nor is &quot;freezing&quot;, as the app is used regularly. Fifth: There is a related question for my GTalk example:  However, I want the opposite: No update.  It might very well be that &quot;Google Apps&quot; (and other pre-installed apps) are handled in some specific way, and restore their &quot;market links&quot; themselves somehow. For this case, my question includes: How to prevent that from happening?  Update There's a  discussing the very same issue. Until recently, a work-around for &quot;user installed apps&quot; was to uninstall them and then sideload the .apk – but even that stopped working. Well, re-signing the .apk with a different key might work for user-apps. But both would fail for pre-installed apps (can't sideload them to override; different signature would refuse that install completely). Moreover, there's an  on this by some &quot;joel.bou..&quot;. Not hard to guess, though blanked out: that would be Joël Bourquard. If it's really him, then that's really an issue (for those who don't know: Joël is the dev behind Titanium Backup). Let me quote from the issue:  For the record: in the Android Market days it was possible to &quot;Attach&quot; or &quot;Detach&quot; apps (on rooted devices) with a system tool such as Titanium Backup. But nowadays (with the Google Play Store app) this has become nearly impossible to do, because the complete app list seems to sync from Google's servers and the user has no control over that.  Which explains why detaching with apps like Titanium Backup is no longer permanent. And I'm afraid I've asked the impossible. But I thought the same in the past with other questions, and surprisingly got solutions here. So I do not yet give up hope on this one!  1: what that does is explained by eldarerathis  (thanks to  for digging that up!) Why can't I find a USB-C hub with multiple USB-C ports? My computer only has one USB-C port and I want to connect multiple USB-C devices to it.  I have trawled through Amazon but am amazed that I cannot find a single one. There are many hubs that have USB 3.1 USB-A ports but not USB-C ones.  Is there a limitation in the spec that prevents this being possible? How can I take a photo with everything in focus with my DSLR? I am quite new to DSLRs and one of the first things I noticed was the incredible focus points and appearance of depth that you can achieve. That is great in a lot of scenarios, but not in all. When filming a landscape as a whole, I do not want to have the focus on that single tree, but on the whole skyline.  Is there a way by which you can sort-of "disable" the focus, so that the raw image is recorded without any added blur? I suppose something as simple as this is only a small function you can turn off, but I can't seem to find it in the manual of my camera. Control Android with broken screen from PC What is the optimal order of post-processing steps? Exit from both root and user with one command I know about "not using sudo su -" etc. But let's be honest, almost all of us do it.   So, here is the issue. We can't have root logins enabled, so we have to ssh in as our user then su to root.  Here is the process tree:       1  7897  7826  7826 ?           -1 S     1000   0:00 sshd: josh@pts/0  7897  7898  7898  7898 pts/0     8182 Ss    1000   0:00  \_ -bash  7898  7990  7990  7898 pts/0     8182 S        0   0:00      \_ sudo su -  7990  7991  7990  7898 pts/0     8182 S        0   0:00          \_ su -  7991  7992  7992  7898 pts/0     8182 S        0   0:00              \_  -su  7992  8182  8182  7898 pts/0     8182 R+       0   0:00                  \_ ps axjf   I would like to exit from root, then from my user with one command. Is there a way to do this?  BTW exit &amp;&amp; exit does not work because it exits the shell and doesnt process the rest of the command  josh@ubuntu:~$ sudo su - root@ubuntu:~# exit &amp;&amp; exit logout josh@ubuntu:~$ Bought in, bought on, bought from, bought at? $|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous. My exercise says: Let $f:\mathbb{R} \rightarrow \mathbb{R}$ a continuous function e suppose that exists $k$ such that:  $$|f(x)-f(y)|\geq k|x-y|$$  Then $f$ is bijective and  its inverse is continuous.  Well, there's a Theorem , Invariance of domain, that says   "If $U$ is an open subset of $\mathbb {R^n}$ and $f : U \rightarrow\mathbb{R}$ is an injective continuous map, then $V = f(U)$ is open and $f$ is a homeomorphism between $U$ and $V$".  But I'm not knowing how to proceed...need a clue...Thanks for attention!!! Why is /tmp a symlink to /private/tmp on Mac OS X? In other words, why isn't /tmp just a regular directory, like on Linux or BSD? I understand how it works and I don't mind it, I'm just interested in the (historical?) reasoning behind it.