Find the radius of convergence: $$\sum_{n=0}^\infty z^{n!}$$ I suppose that this serie behaves in a similar way that $\sum_{n=0}^\infty z^{n}$ , so I have that it converges when $|z| &lt; 1 $. Could someone explain me if this approach is correct and give me a more rigorous proof? Thanks in advance
Does anyone know how to find the radius of convergence of the series $\sum\ z^{n!}$, where $z$ is a complex number?  I tried to use the definition: $$\frac{1}{R}=\limsup\left|\frac{a_{n+1}}{a_{n}}\right|$$ but I wasn't successful.
What is the purpose of using a FIFO vs a temporary file or a pipe? From APUE     FIFOs can be used to duplicate an output stream in a series of shell   commands. This prevents writing the data to an intermediate disk   ﬁle (similar to using pipes to avoid intermediate  disk  ﬁles).       But  whereas  pipes  can  be  used  only  for  linear  connections   between processes, a FIFO has a name, so it can be used for   nonlinear connections.      Consider  a  procedure that  needs  to  process  a  ﬁltered  input    stream  twice.   mkfifo fifo1 prog3 &lt; fifo1 &amp; prog1 &lt; infile | tee fifo1 | prog2       We create the FIFO and then start prog3 in the background, reading   from the FIFO. We then  start prog1 and  use tee to  send  its  input    to  both  the  FIFO  and prog2.    How does a FIFO "duplicate an output stream in a series of shell commands"? Isn't this done by tee instead of a FIFO? In the example, mkfifo fifo1 creates a file in the current directory, and fifo1 seems replaceable with a regular file . So what is the point of a FIFO "prevent writing the data to an intermediate disk file"? What do "linear connections" and "nonlinear connections" between processes mean? What does it mean that a FIFO can be used for nonlinear connections, while a pipe can be only used for linear connections between processes?   Thanks. How do I install MATLAB via the ISO? I gave a scammer my telephone number, address, and name. How bad is it? Updated question because old one was embarassing: I saw a spam email from "PayPal" and I didn't realize that it was a phishing attempt. I gave the phishing site my name, telephone number, and email. What could he do with them?  Old question: Well, I saw a spam email, but I didn't realize that it's really a scam at first. I gave him my telephone number, address, and name. What would he do with them? Could he ruin ALL of my reputation with it? Why does Ubuntu 12.10 not detect my Win7 partition? Drush from GitHub stopped working Moderncv package - cventry date width I am writing my CV using moderncv package, everythig is nice but I have a problem with \cventry command. I have something like this:   (it means 2010 - now)  I would want to have this in one line, rather than in two lines. I tried looking into the moderncv style files but with no success. What can I do to achieve the effect I want? How to call a function in a Twig file Abstract algebra book recommendations for beginners. I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved problems and exercises? The lecturer said in this semester, he will cover group theory, ring theory and a bit of field theory. Which book contains extensive information in these three fields? How to determine the size of a package while using apt prior to downloading? When using apt-get install &lt;package_name&gt;, and there are dependencies that need to be downloaded, the terminal outputs names of additional packages and total size, and asks for confirmation before downloading.   But, when dependencies are satisfied and nothing but the named package needs to be downloaded there is no size output and no confirmation.  When using Synaptic, I can see the total size that new packages that will use after installation but no way to see the size that needs to be downloaded, except to go from package to package and use properties to see the compressed size.  I would like to know if there is a way to see the size of a package(s) in terminal and Synaptic prior to downloading and installing it/them? I need to get execution time in milliseconds.  I originally asked this question back in 2008. The accepted answer then was to use  However, we can all agree now  that using the standard  API is more appropriate. I am therefore changing the accepted answer to this one. Export Track Markers to csv I am trying to export markers from the Blender motion tracker and found the following script that will do exactly that:  for clip in D.movieclips:     for track in clip.tracking.tracks:         fn = 'data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name)         with open(fn, 'w') as f:             frameno = 0             while True:                 markerAtFrame = track.markers.find_frame(frameno)                 if not markerAtFrame:                     break                 frameno += 1                 coords = markerAtFrame.co.xy                 f.write('{0} {1}\n'.format(coords[0], coords[1]))   It works but I have two questions:   How can I save the data on my Desktop rather than in folder in MacOS blender content where it saved right now. The following won't work:   fn = '/User/me/Desktop/data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name) The resulting values I get do not represent the more user friendly marker values in den Blender GUI. Instead of x/y coordinates in screen coordinates, I get a value between 0/1. How can I convert them to those screen coordinates ?    Thanks for your help I try to create a common extent for rasters in QGIS 2.99. Here is my script:  import processing  processing.runalg("script:unifyextentandresolution",                   "/qgis_data/rasters/Image2.tif;                   /qgis_data/rasters/Image1.tif",                  -9999,"/qgis_data/rasters",True)   However, processing.runalg is being used for QGIS 2.99. I need it for QGIS 2.99 What are the grammatical rules determining whether to use which or what?  I usually go by intuition. It's "What car are you looking at?" and "What bicycle do you like most?" but "Which song did you sing?" Quite often, I don't know whether to use what or which.  How can I tell? Fortunately, I can still login with this email address that I have lost access to.  I have been searching around here for a way to update it to the current one I use.  I have found many answers.  But they all give instructions to click on something not displayed or in one case, a page that prompts me to login via another email I no longer have the password for. I need current up to date instructions on how to change my email address or add another email-based login for this same user name that I am posting this with. Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken? Texture is missing in Cycles? Because I am pretty new to blender I watched the tutorial  from BlenderCookie.com.  I loaded  onto a sphere but then in all views the texture is just some kind of blurry with no details. UK visa blank refusal letter without reason for refusal How do I apply a patch file? Does someone know how to set a command block with a command inside using the setblock command?  I have created this code /setblock &lt;x&gt; &lt;y&gt; &lt;z&gt; command_block {TileEntityData:{Command:"testfor @p[_=1]"}} but it doesn't works.  Do someone know how to do that? How to prove Fibonacci sequence with matrices?