Show that $ \sum_{n\in \mathbb {S}} \frac{1}{n} $ is convergent Let $\mathbb {S} =\left \{ 1,2,3,...,9,11,12,...,19,21,...99,111,112,113... \right \} $ i.e, the positive integers set which contain zero digit is omitted.  Now show that $ \sum_{n\in \mathbb {S}}  \frac{1}{n} $ is convergent .  I really don't have no idea about how to prove this
Sum over all non-evil numbers I'm working on the following contest math problem:     Define an evil number to be any positive integer that contains the   digit $9$. Show that      $$ \sum_{x} \frac{1}{x} &lt; 80 $$      where the sum is over all non-evil positive integers $x$.   I'm very confused on where to begin. Initially, I tried to consider this sum as part of the sum of $1/x$ over all positive integers, namely by noting that  $$ \sum_{n=1}^{\infty} \frac{1}{n} = \sum_{x} \frac{1}{x} + \sum_{y} \frac{1}{y} $$  where the first summation on the right side is the same as in the problem statement and the second is the sum over all evil numbers. However, I can't seem to find a way to use this since the sum of the left diverges.  Could anyone lend a helping hand?
Rewrite rules goes away How can I make Firefox open magnet-links in Transmission? I can't find out how to make Firefox open magnet-links in Transmission.   There is no option to make it the standard program for magnet-links in its properties, and as I am not experienced with the filesystem so I can't add it as the standard program in Firefox either. In Java, for a string x, what is the runtime cost of s.length()? Is it O(1) or O(n)? I've been told that code such as:  for (int i = 0; i &lt; x.length(); i++) {     // blah }   is actually O(n^2) because of the repeated calls to x.length(). Instead I should use:  int l = x.length(); for (int i = 0; i &lt; l; i++) {     // blah }   Is this true? Is string length stored as a private integer attribute of the String class? Or does String.length() really walk the whole string just to determine its length? Can't delete folder in Windows 7 What is the most preferred and easiest way to do pagination in ASP.NET MVC?  I.e. what is the easiest way to break up a list into several browsable pages.  As an example lets say I get a list of elements from a database/gateway/repository like this:  public ActionResult ListMyItems() {     List&lt;Item&gt; list = ItemDB.GetListOfItems();     ViewData["ItemList"] = list;      return View(); }   For simplicity's sake I'd like to specify just a page number for my action as parameter. Like this:  public ActionResult ListMyItems(int page) {    //... } Proof that $\suṃ̣_{k=1}^{n}k {n \choose k}$ for $n \in \mathbb N$ is equal to $n2^{n-1}$.  As a hint I got that $k {n \choose k} = n {n-1\choose k-1} $.  I tried solving this by induction but, in the inductive step I'm not arriving to the correct result. How does vendor restocking work in Fallout 4? I've been looking for 2mm EC ammo and according to the  it is supposed to restock every 48 hours at Arturo. However he has not gotten any new 2mm EC ammo for at least 10 restocks.   Do vendors restock on a random selection of items with some being more likely than others? Is there a max limit to how many different items a vendor will sell so that no new items will be added to stock after this limit is reached? Is there a level limit on what items can be restocked? I bought 2mm EC ammunition once from Arturo so I assume I'm high enough level if that's the case? What causes "java.lang.IllegalStateException: Neither BindingResult nor plain target object for bean name 'command' available as request attribute"? chown -R root.root / So I was working and there was a directory that I was periodically changing to my user in  a root terminal so that I could open the files in text editors, but I accidentally pressed / instead of . and this was the command I put out:  chown -R emil.emil /   Then immediately panicked ^C and put in another command, as I thought I could always change back the files I needed to access:  chown -R root.root /   So now I can't do su from emil to even try to fix this, as I'm getting permission denied error. I'm on Ubuntu could someone tell me if there is a way I could fix this, without absolutely reinstalling the whole thing.  TIP  If you are trying to get root access, and are getting this permission denied error when using su try this command:  gksu gnome-terminal   It will prompt you for the root password and open a new root terminal for some reason this works and gives me root access, when su doesn't. I was wondering if there is any way to escape a CDATA end token (]]&gt;) within a CDATA section in an xml document. Or, more generally, if there is some escape sequence for using within a CDATA (but if it exists, I guess it'd probably only make sense to escape begin or end tokens, anyway).   Basically, can you have a begin or end token embedded in a CDATA and tell the parser not to interpret it but to treat it as just another character sequence.  Probably, you should just refactor your xml structure or your code if you find yourself trying to do that, but even though I've been working with xml on a daily basis for the last 3 years or so and I have never had this problem, I was wondering if it was possible. Just out of curiosity.  Edit:  Other than using html encoding... How do I merge 2 VMware disks in to a single one? I have installed an Ubuntu server on a VMWare workstation with a space of 20GB storage as seen below:    After the installation I've attached another 40GB worth storage to the existing Ubuntu server installation (seen below):    Now I want to add this 40GB to my / (root) directory it mean's  I want that my / directory became to 60G , like it will be resize from 20G to 60G (20G + 40G), i don't know what should i do, can any body help me ?  , my df -h result shows;  root@Userver:~# df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda1        18G  900M   16G   6% / udev            990M  4.0K  990M   1% /dev tmpfs           400M  308K  399M   1% /run none            5.0M     0  5.0M   0% /run/lock none            999M     0  999M   0% /run/shm none            100M     0  100M   0% /run/user root@Userver:~#   it must be 60G !  i have no graphic mode, then i can't use Gparted tools, i'm just have ssh access ! Upgrading from a modern smartphone camera without going all in on a DSLR kit I am interested in determining the ages of all 70+ my servers. I would like to create a growth graph showing when servers and databases were added to the environment either/both monthly or annually. I executed the following query using the SSMS multi-query feature with only partial success.  SELECT [name], create_date FROM sys.databases   It's partial success because the master and model databases return with a date of 'April 8, 2003' when I know that I created some of these servers during the past couple years.  I refresh databases from one server to another several times a week, which appears to be causing issues with the database create date.   Is there a simple method to determine the actual create date for both servers and databases? Spurious @ symbol at start of bash prompt in Debian Jessie 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. Can't find wifi drivers for 0bda:f179 Realtek Semiconductor Corp Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$. I don't know how to solve this problem. I tried to write out the sum of products in the definition of products of ideals, but that doesn't seem to lead anywhere. how to use common modulus attack? I am struck with the following problem:  Let Alice, Bob, Chris and Eve communicate over a public network. They encrypt all messages they send using RSA system. Bob and Chris have the RSA modulus $n_B$ and $n_C$ respectively with $n_B$ = $n_C$ But different public encryption exponents: $e_B \neq e_C$. Suppose $\gcd(e_B, e_C)=1$, and that Alice sends the same secret message to Bob and Chris. Show how Eve can decipher the message. Windows vs Linux Local Time? Is there a quick way to get the control that's under the mouse? I need to find the control under the mouse, within an event of another control.  I could start with GetTopLevel and iterate down using GetChildAtPoint, but is there a quicker way?