Prove that $\sum_n f_n$ uniformly converges.
Uniform convergence of alternating series
Do we have different badges in different SE sites I'm trying, but something is wrong with my code in LaTeX: \begin{asy} pair dynkinMark(real x, real y, string s = &quot;&quot;, pen p = defaultpen, pair B = dir(45)) { if (s != &quot;&quot;) { dot(&quot;$&quot;+s+&quot;$&quot;, (x,y), B, p); }     else { dot((x,y), p); }     return (x,y); }  dynkinMark(0,1, &quot;1&quot;, dir(135)); dynkinMark(0,2, &quot;2&quot;, dir(135)); dynkinMark(0,3, &quot;3&quot;, dir(135)); dynkinMark(0,4, &quot;4&quot;, dir(135)); dynkinMark(7,1, &quot;1'&quot;); dynkinMark(7,2, &quot;2'&quot;); dynkinMark(7,3, &quot;3'&quot;); dynkinMark(7,4, &quot;4'&quot;); path p1 = (0,1)..(2,2.0)..(5,3.5)..(7,4); path p2 = (0,2)..(2,1.2)..(5,2.5)..(7,3); path p3 = (0,3)..(2,2.8)..(5,1.5)..(7,1); path p4 = (0,4)..(2,3.8)..(5,3.5)..(7,2); draw(p1, blue); draw(p2, heavycyan); draw(p3, mediumcyan); draw(p4, lightblue); dot(&quot;$12$&quot;, IP(p1, p2), dir(90), heavygreen); dot(&quot;$13$&quot;, IP(p1, p3), dir(90), heavygreen); dot(&quot;$23$&quot;, IP(p2, p3), dir(90), heavygreen); dot(&quot;$14$&quot;, IP(p1, p4), dir(90), heavygreen); dot(&quot;$24$&quot;, IP(p2, p4), dir(90), heavygreen); real y = 0.8; label(&quot;$s_1$&quot;, (IP(p1,p2).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p1,p3).x, y), heavygreen); label(&quot;$s_1$&quot;, (IP(p2,p3).x, y), heavygreen); label(&quot;$s_3$&quot;, (IP(p1,p4).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p2,p4).x, y), heavygreen); \end{asy} I know that if you create a custom object, with an Auto-number Name field with a format, e.g. MYC-{0000} you will be able to create records from MYC-0000 to MYC-9999.  The moment you create 10,000 records Salesforce happily extends the range and you can then create MYC-10000 to MYC-99999.  My question is, what is the limit to this - for obvious reasons its a difficult one to test. I know instances that have exceeded 999,999 e.g. MYC-1000000 but am interested to know how far this extends to.  EDIT: When the field has a data type of Text the maximum length is 80. Is it safe to assume that the same is true for Autonumber (though that would be a very big number)? Take a screenshot of a webpage with JavaScript? Does "She had a brother" mean that her brother is dead? My Friend has sent me this riddle to solve:     "If you solve this, then you are a genius. Mr.Smith has 4   daughters🙍‍♀🙍‍♀🙍‍♀🙍‍♀ and each daughter had a brother.  How many   children does Mr. Smith have now?"   He said the answer is not 5, but 4 only as in the riddle it is mentioned as each daughter had a brother. So their only brother is dead.     Is he right? In what order are the dated ordered by? Certainly not alphanumeric order.  ls -lt sorts by modification time. But I need creation time. I use this program in Windows that's one-box and searches all of my drives. By default it lists all files, everywhere, in a single list. Is there a Linux graphical utility that does this? Android OS without Google Services? I have a Sony Xperia Z with version 4.1.2 running.  My question is about removing all of the Google baggage from the phone.  I have no Google account tied to my phone and would really like to get rid of all traces of Google from my phone for a few reasons:   Battery performance: Google services ranks in the top 3 of what uses up my battery Privacy: I try to minimize what Google siphons from my phone with the exception of Google maps Less Dependency: I don't want to be dependent on one company for all my needs.   So are there any Android versions out there that are minimalistic and do not invade your privacy? Windows 7: Disable Lock Workstation After 10 Minutes Using Group Policy On my Windows 7 PC the system becomes locked after 10 minutes of inactivity. Usually I would find this setting next to the screen-saver configuration. The setting is grayed out, however.  I think this is because of corporate group policy. As I am an administrator on this computer I should be able to reconfigure the group policy setting using gpedit.msc.  What is the group policy setting that I need to change to prevent automatic locking of my workstation?  Edit: I don't have configured a screen-saver. I also want to continue to be able to lock the workstation manually. Why does latex stretch small sections across the whole page vertically? There's a part in my apps that displays the file path loaded by the user through OpenFileDialog. It's taking up too much space to display the whole path, but I don't want to display only the filename as it might be ambiguous. So I would prefer to show the file path relative to the assembly/exe directory.  For example, the assembly resides at C:\Program Files\Dummy Folder\MyProgram and the file at C:\Program Files\Dummy Folder\MyProgram\Data\datafile1.dat then I would like it to show .\Data\datafile1.dat. If the file is in C:\Program Files\Dummy Folder\datafile1.dat, then I would want ..\datafile1.dat. But if the file is at the root directory or 1 directory below root, then display the full path.   What solution would you recommend? Regex?  Basically I want to display useful file path info without taking too much screen space.  EDIT: Just to clarify a little bit more. The purpose of this solution is to help user or myself knowing which file did I loaded last and roughly from which directory was it from. I'm using a readonly textbox to display the path. Most of the time, the file path is much longer than the display space of the textbox. The path is supposed to be informative but not important enough as to take up more screen space.  Alex Brault comment was good, so is Jonathan Leffler. The Win32 function provided by DavidK only help with part of the problem, not the whole of it, but thanks anyway. As for James Newton-King solution, I'll give it a try later when I'm free. Several airline and trip planning sites will allow you to check "I am flexible with my dates" or a similar option.  Is there any way to also search more broadly for location?  For example, if you wanted to leave from YYZ or YKF and arrive at any airport in California, can a search for such flights be done somehow?  I ask because when I plan plane trips, I want the lowest price.  I'm OK with leaving a day or two later if I save $200 (same with the return trip).  There are 3 airports within 80 km of me, I'll leave from the one with the cheapest flight. And I'm also OK with changing the trip to spend time exploring San Francisco instead of lying on the beach near San Diego, and that sort of thing.  Normally this would take dozens of searches, but I'd like to see it all at once. How to loop over the lines of a file? Say I have this file:  hello world hello world   This program  #!/bin/bash  for i in $(cat $1); do     echo "tester: $i" done   outputs  tester: hello tester: world tester: hello tester: world   I'd like to have the for iterate over each line individually ignoring whitespaces though, i.e. the last two lines should be replaced by  tester: hello world   Using quotes for i in "$(cat $1)"; results in i being assigned the whole file at once. What should I change? While I can post external texts into question and answer bodies, it preserves the old font style, spacing and size (although the markdown display won’t be affected by that.)   App Version: 1.6.6.2 Device: iPhone 6 OS Version: Version 11.0.3 (Build 15A432) Tips and resources for beginning designers How to rename partitions? I'm new at Ubuntu; I installed Ubuntu 12.10 and the partitions appear like 30 GB volume and like 78EF-2C5E in task bar. I tried to rename it but rename and remove buttons are deactivated so I tried by using disks but it gives me error:  (Error setting label: Command-line `mlabel -i "/dev/sdb8" ::"windows"' exited with non-zero exit status 1: Total number of sectors (18550784) not a multiple of sectors per track (63)! Add mtools_skip_check=1 to your .mtoolsrc file to skip this test  (udisks-error-quark, 0))   and this happen also to any attached usb to my laptop. Picking random points in the volume of sphere with uniform probability If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues? Editing question title creates whole new question and other question list problems What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.