I was given this series:  Let $q \in \mathbb{C}, \mid q\mid &lt;1. $  $$\frac{1}{2}\sum_{n=0}^{\infty} (n^2 +3n +2)q^n $$  Now I have to show that   $$\frac{1}{(1-q)^3}=\frac{1}{2}\sum_{n=0}^{\infty} (n^2 +3n +2)q^n$$  and proof whether or not this series converges absolutely.  For the convergence I guess I have to use one of the many convergence criteria and for the equality I have no clue how to even start.
Use Cauchy product to find a power series represenitation of   $$1 \over {(1-x)^3}$$ which is valid in the interval $(-1,1)$.   Is it right to use the product of $1 \over {1-x}$ and $1 \over {(1-x)^2}$ if I know thier expantion (HOW).. Is there another way?
Why are the longer edges being beveled more? I'll preface this by saying I'm very new to Blender - I'm trying to put a bevel on an edge, looks something like this:    As you can see, the vertical side is much longer than the horizontal side.  When I apply to bevel to the edge there, the bevel stretches proportionally - so there's 'more' bevel on the longer side.  I want to bevel without any 'ratio' like that - just a 45-degree bevel, if that makes any sense.  Do I have to put in a loop cut to make the side lengths equal?  I tried using a sub-surf modifier, but it applies on a bunch of nearby edges, when I just want to round this one corner. How to do joins in LINQ on multiple fields in single join Account "last activity time" is not always updated It would appear that the account's "Last activity time" is not updated for every hit.  I've been active on SO all morning, and in the last five minutes have voted on some posts as well as posted an answer.  However,  says:     "Last activity: 2 hours ago from &lt;IP address&gt;"   Is there a certain amount of time that needs to elapse between hits before the activity time is updated again?  This issue could result in Enthusiast badges not being awarded when they should. What issues should be considered when overriding equals and hashCode in Java? Slope layer with false results in QGIS? After the DEM creation, I wanted to create slope layer.   However, the result has not satisfied me. I don't think the slope map is correct. Have you ever encountered false calculated terrain map?  This is the DEM:    And this is the slope layer. Can one PC throw another? For example, if there is a lava river surrounding a castle. There is a drawbridge that can be lowered, but the lever is on the other side. PCs couldn't find a hidden passageway,either because PCs failed necessary check and couldn't find it or just because there isn't one. They don't have rope to try to pull the lever down. Or if PCs want to rob a house, but can't pick a lock, they see that window on the second floor is open. Can one PC use his Strength to throw another PC that is one size smaller, with other PC using his Dexterity or Strength to not fall down or lose balance? How do I monitor the computer's CPU, memory, and disk usage in Java? I would like to monitor the following system information in Java:   Current CPU usage** (percent) Available memory* (free/total) Available disk space (free/total)  *Note that I mean overall memory available to the whole system, not just the JVM.   I'm looking for a cross-platform solution (Linux, Mac, and Windows) that doesn't rely on my own code calling external programs or using JNI. Although these are viable options, I would prefer not to maintain OS-specific code myself if someone already has a better solution.  If there's a free library out there that does this in a reliable, cross-platform manner, that would be great (even if it makes external calls or uses native code itself).  Any suggestions are much appreciated.  To clarify, I would like to get the current CPU usage for the whole system, not just the Java process(es).  The SIGAR API provides all the functionality I'm looking for in one package, so it's the best answer to my question so far. However, due it being licensed under the GPL, I cannot use it for my original purpose (a closed source, commercial product). It's possible that Hyperic may license SIGAR for commercial use, but I haven't looked into it. For my GPL projects, I will definitely consider SIGAR in the future.  For my current needs, I'm leaning towards the following:   For CPU usage, OperatingSystemMXBean.getSystemLoadAverage() / OperatingSystemMXBean.getAvailableProcessors() (load average per cpu) For memory, OperatingSystemMXBean.getTotalPhysicalMemorySize() and OperatingSystemMXBean.getFreePhysicalMemorySize() For disk space, File.getTotalSpace() and File.getUsableSpace()   Limitations:  The getSystemLoadAverage() and disk space querying methods are only available under Java 6. Also, some JMX functionality may not be available to all platforms (i.e. it's been reported that getSystemLoadAverage() returns -1 on Windows).  Although originally licensed under GPL, it  to , which can generally be used for closed source, commercial products. fontawesome and pdflatex When using pdflatex and the fontawesome package the below error shows up.   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! Fatal fontspec error: "cannot-use-pdftex" !  ! The fontspec package requires either XeTeX or LuaTeX to function. !  ! You must change your typesetting engine to, e.g., "xelatex" or "lualatex" ! instead of plain "latex" or "pdflatex". !  ! See the fontspec documentation for further information. !  ! For immediate help type H &lt;return&gt;. !...............................................     Wish to keep on using "pdflatex" instead of "xelatex" or "lualatex".   In fontawesome Version 4.4.0 manual it says "When using the (pdf)(LA)TEX engine, the fontawesome package doesn’t require any external package".  Tried solutions proposed for this question () without success.   MWE:  \documentclass{article} \usepackage{fontawesome} \begin{document} {\faAdjust} \end{document} Analysing the "kind(s) of problem(s) are [ones]/[to be]" construction A. These kinds of problem are to be avoided. B. These kind of problems are to be avoided.  Are both A and B grammatical? If not, why not? If so, after having noticed the parallelism between A and C, and between B and D, could we say that C and D are &quot;standard&quot; English, too?  C. These kinds of problem are ones to avoid. D. These kind of problems are ones to avoid. Is there any way to run file explorer as administrator under Windows 10 After install Windows 10, it seems that I lost the ability to run explorer.exe as administrator with a user in administrator group.   The reason I want to do that is, in our team's development environment, we are using a C# exe to do some environment configuration which will start command prompt under administrator mode and subst a drive. As a result those substed drives are not visible within the file explorer since it is run not as administrator. That will be kind of inconvenience and sometimes make mistakes.   I was able to run explorer.exe from task manager with the option "create with privileges" checked and then I can see all the drives in explorer. But now this is not working anymore.   I knew there are other options to workaround this workflow, but just want to make sure that if it is now totally impossible under Windows 10?  Any comment is appreciated. How can I make a fake name when I use command blocks? I'm trying to make a mini game but I want it so that when you press a button over a command block it will say "BOB welcome", so 'bob' instead of the @a or @p sign and then followed by the message. All I know is that I need to use /tellraw. Honey changing into unusable, hardened clump Star vs Heart icon to represent save as a favourite I am working on a mobile app that involves the user saving a favourite location. I wanted to use an icon to represent that feature, but I'm not sure which one is better – a star or a heart icon.  Some say heart icon tends to increase the rate of productivity, and some say they are used to a star icon to 'save' or 'bookmark' something.  What do go you guys think? I read a story once about a man who escapes from his pursuers by doing an uncontrolled jump into hyperspace. If I'm not mixing my stories up he was blind but could see through the eyes of other sighted people/animals nearby. He was able to see through his pet but it dies and he thinks he's finished - he's blind and lost in hyperspace but there's a rat on board which he eventually catches by turning off gravity and then he can see through the rat's eyes. He works out how hyperspace operates and can hop back to where he came from.   Can anyone remember the name of the story and the author? I enjoyed it when I was a kid and would like to read it again. Work out the type of c# application a class contained in a DLL is being used by Beta regression of proportion data including 1 and 0 Do GTA 5 saves back-up to a cloud service? For GTA 5 (on PC), if I have a save file, will it automatically back-up to either the Steam or Rockstar cloud, or do I have to save it manually? If it have to save it manually, will you please provide the default directory for saves? Last months I have lots of referrer spammers in my GA statistics. Their count is ~10x higher than count of legit visitors (my site is not very popular yet). I've turned on an option to hide known spammers in GA settings, but it didn't help at all. It seems these spammers are using scripts to spam directly to GA (i.e. they are not logged in my IIS).  Is there anything I can do to stop these spammers?    UPD 10 months later, and they started spamming using fake target page names... and Google is still doing nothing about it. Sending Text Cross Domain By Bookmarklet Find an example of a function sum $\sum_{n=1}^\infty u_n $ that converges   uniformly on $[a,b]$ and converges absolutely pointwise, but   $\sum_{n=1}^\infty |u_n| $ doesn't converge uniformly on $[a,b]$.   This seems pretty straightfoawrd but it's really hard to find an example. The choice of $u_n$ must be very specific. You can actually prove any power series wont work (due to Abel's theorem)  In addition, in order to prove the uniform convergence, $u_n$ must not satisfy Weierstrass' M-Test (because then $\sum |u_n|$ would converge uniformly aswell)