How to solve this summatory?: $$\sum _{n=0}^{\infty }n^2\:0.999^{n-1}\cdot 0.001$$  I know how to calculate this one: $$\sum _{n=0}^{\infty }n\:0.999^{n-1}\cdot 0.001$$ as a sumatory of an arithmetic-geometric progression, but I don't know how to calculate this one with the square.
I'd like to find out why  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6 \end{align}  I tried to rewrite it into a geometric series  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = \sum_{n=0}^{\infty} \Big(\frac{1}{2}\Big)^nn^2 \end{align}  But I don't know what to do with the $n^2$.
How can I delete a symbolic link? I created a symlink using mklink.  Now I need to change it but I can't figure out how to delete it so I can recreate it correctly. How to delete a non-empty directory in Terminal? Idempotents in a ring without unity (rng) and no zero divisors. Question: Given a ring without unity and with no zero-divisors, is it possible that there are idempotents other than zero?   Def: $a$ is idempotent if $a^2 = a$.   Originally the problem was to show that $1$ and $0$ are the only idempotents in a ring with unity and no zero-divisors, but I wonder what happens if we remove the unity condition.   I am trying to find a ring with idempotents not equal to $0$ or $1$. So far my biggest struggle has been coming up with examples of rings with the given properties.   Does anyone have any hints? How should I attack this problem? Very strange error suddenly appeared running Biber Backquote in lsblk output What does ` mean in this output from lsblk? How to secure recommendations and apply for PhD after having worked outside of academia for two years? Drift velocity of electron Best way to clone an installation (copying to identical hardware) Kind-of like  but slightly different (I think), in that I have 6 identical Acer Aspire Revo R3610 machines. One is (almost) configured to my requirements - when I'm done preparing it I'd like to make the other 5 machines absolutely the same. I'm very new to Ubuntu, what's the most straightforward (easiest) way of doing this?  The machines are going to live on different networks if that might otherwise be a problem (eg with Windows you can clone disks but you then have to make registry changes afterwards if they're going to run on the same network etc). The hardware in all 6 machines is, I stress, the same!  How can I efficiently clone one source image on to these identical machines?  Please restrict one software/solution per answer While trying to ask a question, I got the error message     This question body does not meet our quality standards. Please make sure that it completely describes your problem - including what you have already tried - and is written using proper grammar.    Why am I getting this message? What can I do to get the system to accept my question? Can you be more specific? What are good resources on how to ask high-quality questions?      For more information, see  in the . Examples of Bayesian and frequentist approach giving different answers Note: I am aware of  differences between Bayesian and frequentist statistics. For example &quot;what is the probability that the coin on the table is heads&quot; doesn't make sense in frequentist statistics, since it has either already landed heads or tails -- there is nothing probabilistic about it. So the question has no answer in frequentist terms. But such a difference is specifically not the kind of difference I'm asking about. Rather, I would like to know how their predictions for well-formed questions actually differ in the real world, excluding any theoretical/philosophical differences such as the example I mentioned above. So in other words: What's an example of a question, answerable in both frequentist and Bayesian statistics, whose answer is different between the two? (e.g. Perhaps one of them answers &quot;1/2&quot; to a particular question, and the other answers &quot;2/3&quot;.) Are there any such differences?  If so, what are some examples?  If not, then when does it actually ever make a difference whether I use Bayesian or frequentist statistics when solving a particular problem? Why would I avoid one in favor of the other? Minecraft item right/left click detection LINQ's Distinct() on a particular property I am playing with LINQ to learn about it, but I can't figure out how to use Distinct when I do not have a simple list (a simple list of integers is pretty easy to do, this is not the question). What I if want to use  on a list of an Object on one or more properties of the object?  Example: If an object is Person, with Property Id. How can I get all Person and use Distinct on them with the property Id of the object?  Person1: Id=1, Name="Test1" Person2: Id=1, Name="Test1" Person3: Id=2, Name="Test2"   How can I get just Person1 and Person3? Is that possible?  If it's not possible with LINQ, what would be the best way to have a list of Person depending on some of its properties in .NET 3.5? Is there a package that automatically inserts the ToC level of the reference I inserted?  Section 1.1 \label{a} Subsection 1.1.1 \label{b} Subsection 1.1.2  \label{c}   So that the text:  Blah \superref{a} and \superref{b} and \superref{c}   becomes:  Blah Section 1.1 and Subsection 1.1.1 and Subsection 1.1.2   So that it automatically adapts if I change the level of a label? php sort associative arrays by keys that those keys exist in other array I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help Bash: command not found So a buddy and I were playing a game of Magic that turned out to be a really quick game because he got  out on the battlefield early. He was tapping it without attacking because of its obviously awesome ability but I don't know if you can tap a creature for its Inspired (untap-triggered) ability without attacking for it to then be tapped. Are you allowed to tap a creature whenever you want? Where is the "Manipulate Centers Only" button in Blender 2.8? I have looked just about everywhere on the Internet and I can't find the answer to this question. Where the hell is the "Manipulate Centers Only" button in Blender 2.8???? It's the the double arrow icon here:    I seem to have enabled it somehow and I can't scale or rotate my object. How do I easily switch between windows rather than applications in GNOME Shell? How to use LyX to create PDF file from the command line