How does one evaluate $\sum_{t=1}^\infty tr^t$?
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
Homomorphism between free groups Let $F_a$ be the group which is freely generated by $a$ elements. How to show that there is a homomorphism from $F_a$ onto $F_b$ if and only if $b\le a$?  I was thinking one possibility is if $F_a$ generated freely by $\{x_1, \dots , x_a\}$ and $F_b$ generated freely by $\{y_1, \dots , y_b\}$ then consider map which says $\phi(x_i)=y_i$ for $1\le i \le b$ and $y_1$ otherwise. I do not know if this works or even how to proceed. How to show this fact? I am trying to fit a SVM to my data. My dataset contains 3 classes and I am performing 10 fold cross validation (in LibSVM):   ./svm-train -g 0.5 -c 10 -e 0.1 -v 10 training_data   The help thereby states:  -c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)   For me, providing higher cost (C) values gives me higher accuracy. What does C in SVM actually mean? Why and when should I use higher/lower values (or the LibSVM given default value) of C? A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular? A cardinal $\kappa$ such that $2^{\lambda}&lt;\kappa$ for all $\lambda&lt;\kappa$ is regular?  I would appreciate very much an answer Seems like a stupid question, but I'm after a nice solid answer if possible.  I joined SO a while ago to ask the odd question, but recently I'm starting to use it more often.  I've been reviewing the 40 max items (20 first posts/20 late answers) per day, and editing anything I see wrong with them (lots of +2's)... flagging them... etc.  I've also been  per day.  But other than commenting where I can and answering the odd question, I'm only  (1k at the moment).  I might just be overeager, but I was hoping some high-rep users might be able to write a little something on how they earned their stripes?  I've , and to be honest I was hoping I'd get a hit, because it sounds like a stupid question... anyways, here you go!  Also, I'm not referring to how to gain rep on Meta, since it's a bit of a fluke I've earned the rep I have on here. I'm asking about main SO. Even my main monitor is shown as unknown. I have tried setting up dual monitors using Nvidia settings with no joy however it does recognize that I have 2 monitors.  This was not an issue in 11.04. My problem with the Nvidia settings appears to be that my 2 monitors require different resolutions but even when I set them to a resolution that they both can handle, it is then only appearing in cloned mode. I really hope someone can help or I will have to roll back to 11.04.  Why won't Ubuntu 11.10 recognize that I have 2 Monitors?   Here is the contents of my xorg.conf:  # nvidia-settings: X configuration file generated by nvidia-settings # nvidia-settings:  version 280.13  (buildd@rothera)  Thu Aug 11 17:28:49 UTC 2011  Section "ServerLayout"     Identifier     "Layout0"     Screen      0  "Screen0" 0 0     InputDevice    "Keyboard0" "CoreKeyboard"     InputDevice    "Mouse0" "CorePointer"     Option         "Xinerama" "0" EndSection  Section "Files" EndSection  Section "InputDevice"     # generated from default     Identifier     "Mouse0"     Driver         "mouse"     Option         "Protocol" "auto"     Option         "Device" "/dev/psaux"     Option         "Emulate3Buttons" "no"     Option         "ZAxisMapping" "4 5" EndSection  Section "InputDevice"     # generated from default     Identifier     "Keyboard0"     Driver         "kbd" EndSection  Section "Monitor"     # HorizSync source: xconfig, VertRefresh source: xconfig     Identifier     "Monitor0"     VendorName     "Unknown"     ModelName      "CRT-0"     HorizSync       30.0 - 83.0     VertRefresh     50.0 - 76.0     Option         "DPMS" EndSection  Section "Device"     Identifier     "Device0"     Driver         "nvidia"     VendorName     "NVIDIA Corporation"     BoardName      "GeForce 7025 / nForce 630a" EndSection  Section "Screen"     Identifier     "Screen0"     Device         "Device0"     Monitor        "Monitor0"     DefaultDepth    24     Option         "TwinView" "1"     Option         "TwinViewXineramaInfoOrder" "CRT-0"     Option         "metamodes" "CRT: 1280x1024 +1024+0, DFP: 1024x768 +0+0"     SubSection     "Display"         Depth       24     EndSubSection EndSection"   ok I have tried disper -e. Problem is that Nvidia settings appear to be treating both monitors as the same one. so changing the settings to one has no effect, but change the other and it affects both screens identically.  Results of disper -l as follows:      carter@carter-desktop:~$ disper -l display DFP-0: HP vs17  resolutions: 320x240, 400x300, 416x312, 512x384, 576x432, 680x384, 640x480, 720x450, 640x512, 800x512, 840x525, 800x600, 960x540, 832x624, 960x600, 896x672, 1024x768, 1152x864, 1280x960, 1280x1024 display CRT-0: CRT-0  resolutions: 320x240, 400x300, 416x312, 512x384, 576x432, 680x384, 640x480, 720x450, 640x512, 800x512, 840x525, 800x600, 960x540, 832x624, 960x600, 896x672, 1024x768, 1152x864, 1360x768, 1280x960, 1440x900, 1280x1024, 1400x1050, 1600x1024, 1680x1050, 1600x1200, 1920x1080, 1920x1200, 1792x1344 carter@carter-desktop:~$ Why do some Kree have white skin? This seems bizarre to me.  All the Kree we've seen thus far (MCU based) were blue skinned... Ronan the Accuser being the most famous  What do Kree people look like?  Is there anything concrete with their appearance?  It seems odd that Danvers (Captain Marvel) and Jude Law's character (Yon-Rog?) and the "Supreme Intelligence" are all white skinned. Windows says RAM ran out while there is still 4 GB of physical memory available No border-spacing before first item and after last item I was trying to install Ubuntu 12.04 in VirtualBox 4.2.12r84980. I see    this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot   But I am using a 64 bit Windows 8, and trying same .iso for trying Ubuntu. Then what is the problem? How can I customize the Ubuntu installer? So I'm going to be starting a Job here in a few weeks, I've been doing QA for about 6 years now. Pretty much your standard Test Plans/Testing with a little normal SysAdmin stuff that sometimes comes with the task. I've had some good ideas implemented in companies, as far as tracking requirements/test plans/issues differently, and they seem successful. However, this new position will be me laying down the foundation for QA. Right now things are done in what seems to be as needed as far as QA goes, requirements are gathered and sometimes kept in different locations, same with test plans (which are done by developers right now). So my job will be sort of centralizing this, or developing a Flexible way of QA'ing the Software (Web/Mobile development). So it seems the challenge will be centralizing everything, while creating test plans/ or ways of testing similar requirements that is flexible enough to span projects. I've had a few ideas, however, all my previous test work was windows based (So test plans in TFS or Microsoft Test Manager). I wanted to get some ideas from everyone here, or anyone that has started a QA department from scratch. I was also going to see if there were any books on the subject. My thoughts were mainly keeping projects separated for issue tracking (not sure of the software we will use yet). And keeping test plans for common I guess &quot;actions/elements&quot; that are repeated between different customers and executing those. Eventually maybe using selenium to save those &quot;common&quot; elements as test scripts. But I've never set something up like this before solo, so I've been doing quite a bit of reading. Any books/suggestions would be appreciated! Do Stack Exchange sites allow editing of comments and posts from other users? Possible Duplicate:         Is this normal behavior in Stack Exchange sites that after just signing up one can edit not only his/her own comments / posts, but also others' comments / posts?  If so, then the Q&amp;A does not look safe to me. Imagine someone maliciously modifying a post and bringing bad reputation on a Q&amp;A member.  Can you check this and perhaps fix it? Why is it wrong to serial voteup someone you like his answers?  Sometimes I just came to stackoverflow to read certain people answers(there are 4 guys currently) I have their profile bookmarked in my browser and in my free time at office I go to their profile and read their answers and learn a lot from them, but because I'm afraid to be a serial voter, I dont voteup them.   I think there is nothing wrong with that, if there is, please let me know. Why wasn't Sauron invisible when he wore the Ring? When Sauron is shown killing Elendil and then being destroyed by Isildur he is clearly not invisible and he is wearing the Ring.  But any time Bilbo or Frodo put on the Ring they went invisible without fail.  Did the Ring change after Sauron was destroyed or is Sauron capable of controlling the rings power unlike anyone else? I'm trying to find out why my application is very slow on a certain machine (runs fine everywhere else). I think i have traced the performance-problems to hard-disk reads and writes and i think it's simply the very slow disk.  What tool could i use to measure hd read and write performance under Windows 2003 in a non-destructive way (the partitions on the drives have to remain intact)? How to make horizontal lists? This might seem like a very simple question, but what is the easiest way to turn a normal vertical list into a horizontal one? Do I say "I study computer science," or "I study Computer Science"? Similarly, "I really liked that computer science course," vs. "I really liked that Computer Science course." I created the shiftcommandn shortcut for Firefox in Syst Prefs to match other browsers' behavior.     It registers in the Firefox Menubar.     But pressing the shortcut opens a new non-private window, and it loads there the first item in my "Top Sites".   I imagine I could create another shortcut to override this behavior, but what is this behavior? I don't see anything highlighted in the Firefox Menubar when I hit the shortcut. Or might there be another solution (other than using a different shortcut to open new private windows)?   Problem exists on both Mojave and High Sierra. Default Firefox shortcut (shiftcommandp) still opens a new private window. Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$ About a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$  If we'll take a line $f(x)=\begin{cases} ax &amp;, x\in\mathbb R\\ 0 &amp;, x=\infty  \end{cases}$ then we'll have a bijection.   But about this function: $g(x)=\begin{cases} x &amp;, x\in\mathbb R\setminus \{0\}\\ 0 &amp;, x=\infty  \end{cases}$ ? it appears to be a bijection and it's even simpler. How to delete all music on my iPhone How do I delete all the music on my iPhone.  I tried doing it through iTunes but it says my collection is not managed by iTunes and I don't want to erase and sync because all my apps are nicely backed up and sorted with iTunes.  I have only seen a way of deleting song by song on the phone.