Where does the second '1' appear in a value of following series?  $\frac{1}{9}+\frac{1}{99}+\frac{1}{999}+\dots$=$\sum_{n=1}^\infty {\frac{1}{10^n-1}}$  I already have a value of    (link)  But I want to know where the second '1' appears without this result.  There is easy way to determine poistion of the second '1'?
What is the value of the series   $\sum\limits_{n=1}^\infty {\frac{1}{10^n-1}}$   and can one find closed forms for the sums   $\sum\limits_{n=1}^N {\frac{1}{10^n-1}}$?   I found that $\sum_{n=1}^N {\frac{1}{10^n-1}} $  =  $\sum_{n=1}^N (\lim_{m\to\infty  }{\frac{10^{-n}-10^{-nm}}{1-10^{-n}}})$  =  $0.111\ldots+0.0101\ldots+\ldots$ but I can't go farther.     The original question is: "Where does the second '1' appear?"
Transparent model when exporting fbx file to Unity So I have this shark model which I animated and ready to export it on fbx and transport it to Unity.  But When I put it on Unity, It looks transparent like this.    Many of the solutions online say that the problem is because of my faces, and they told me to recalculate it or something, but normals are just fine. Is there any other solution?  here's the blend file: I asked a question regarding a very specific feature of a program and whether or not it works with a larger program.  Within hours someone had marked it with "This question may already have an answer here of a similar question, but not related to my question.  The question I asked IS NOT ADDRESSED in the referred-to question. It's frustrating to spend half an hour putting together an intelligent and specific question, and then have someone mark it as a duplicate (or possible duplicate), which apparently causes people to skip over my question. I haven't received any more responses since the question was flagged.   Two questions:  (1) How do I get this flagging removed and (2) what's the best way to prevent these "helpful" flaggings in the future? Prove that $371\cdots 1$ is not prime Prove that $371\cdots 1$ is not prime.   I tried mathematical induction in order to prove this, but I am stuck.  My partial answer:  To be proved is that $37\underbrace{111\cdots 1}_{n\text{ ones}}$ is never prime for $n\geq 1$. Let $P(n)$ be the statement that $37\underbrace{111\cdots 1}_{n\text{ enen}}$ is not prime.  For $n=1$, we can write $371=7\cdot 53$, and therefore $P(1)$ is true. Let $P(k)$ be true for $k&gt;1$. Then we now have to prove that $P(k+1)$ is true.  I found that $37\underbrace{111\cdots 1}_{k\text{ ones}}$ can be written as $37\cdot 10^k+10^{k-1}+10^{k-2}+\cdots +10^0$ and that $37\underbrace{1111\cdots 1}_{k+1\text{ ones}}$ can be written as $37\cdot 10^{k+1}+10^{k}+10^{k-1}+\cdots+10^0$.  I think I'm pretty close to the answer know, but I don't know how to proceed. How can I make a div not larger than its contents? I have one Ethernet port that is wired directly to the router on another level.  However, I want to run a desktop and a server both off this one Ethernet port.  Can anyone tell me the difference between an Ethernet splitter and a switch?    Also, will either the splitter or switch slow down the connection as opposed to just one connection? Will moving blog posts from under an existing category to a new SUBcategory have a negative impact from an SEO POV? Does installing and using Wine open up your Linux platform to Windows viruses? so I am creating a few posts about bearings and wheels, (story so far):      I have now got the wheels, bearings and freehub working.  Started riding to work this morning and I almost couldn't stop at a junction.  Thankfully wasn't going too fast.  I physically can not get the wheel to lock.  I have to use both brakes at full force to get the bike to roll to a stop.  If I only use one brake I would not stop at any junction in time.  Could the cause be any of the following:   Over greased bearings? Over greased axle? not tightened cone hubs enough? not tighted axle enough?   I do not have any grease on the disk brakes them selves.  Rather nervous getting on the bike now.  Don't seem to be doing too well with this bike home fixing thing.  over greased bearings?  EDIT  Forgot to mention that it is hydraulic disk brakes.  EDIT 2  So in the end I took it to the LBS as I didn't have much confidence in my self at this point.  They had to replace the front pads but where able to clean the rear and cleaned the rotors.  (I had tried to clean the rotors but obviously not vigorously enough).  He said it was a bit of a pain to do.  All is working again.  They double checked my wheels and said I had put them back together correctly which is reassuring.  Thanks for all the help I made an svg in Illustrator, but now I want to use it in a website/app but it's a huge size (around 10 MB) how can I decrease the size of it? My illustrator file is pretty big but that because I have some tracing elements underneath. The file also has a big artboard, but when I save should I delete my tracing elements, and decrease the artboard size? AF mirror not flipping on Canon 350D My Canon 350D is no longer raising the AF mirror when it takes a photo.  Instead, it looks like this when the mirror flips up.   This results in a photo that is half black due to the sensor being obscured.  This camera is 9 years old and has never been dropped, mishandled or subjected to harsh temperature or humidity.  Is there any common maintenance I can do to get this thing swinging properly again? What does **Ens** stand for? Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for?  Most of the categories have names that are self explanatory, and maybe this one does too.  But for the life of me I can't think of it, and a Google search was no help. Why does the new review page sometimes shows questions to vote to close without anybody having voted to close it? Why is "chmod -R 777 /" destructive? This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break? Why is the result of a raster calculation integer when it should be decimal? I'm trying to calculate the NDVI using raster calculator, but the result is integer instead of decimal.  NDVI = (NIR - RED)/(NIR + RED)   The result is normally in the range -1 to 1, but when i tried to calculate de result is -1, 0 and 1, and it does not have have any number in between like, -0.9 or 0.1. And i need those values so i can classify the result in term of soil occupation Python, Unicode, and the Windows console EJB 3.1 Dependency Injection Failed Matrices - Conditions for $AB+BA=0$ The Problem Let $A$ be the matrix $\bigl(\begin{smallmatrix}a&amp;b\\c&amp;d\end{smallmatrix} \bigr)$, where no one of $a,b,c,d$ is $0$. Let $B$ be a $2\times 2$ matrix such that $AB+BA=\bigl(\begin{smallmatrix} 0&amp;0\\ 0&amp;0 \end{smallmatrix} \bigr)$. Show that either   $a+d=0$, in which case the general solution for $B$ depends on 2 parameters, or $ad-bc=0$, in which case the general solution for $B$ depends on one parameter.   (this is question 22 of the last matrix exercise of Further Pure Mathematics by Bostock et al.)  Comments Writing $B=\bigl(\begin{smallmatrix} e&amp;f\\ g&amp;h \end{smallmatrix} \bigr)$ and multiplying out I get that    $(a+d)(f+g)+(b+c)(e+h)=0$ $ae+bg+cf+dh=0$   but I am unable to get the required restrictions on $a,b,c,d$. Is there a quick way of doing the problem that doesn't require manual computation? I thought of considering invertible and non-invertible cases but couldn't get anywhere. Help would be much appreciated. Converting string arrays into Map Difference between Loading a class using ClassLoader and Class.forName I'm new to Blender and this site, so I apologize in advance if I'm not following any of the proper etiquette.  I'm no artist, but I'm trying to learn Blender so that I have some programmer art for me to work around in Unity.    I followed a tutorial for making a basic human model, I rigged it with rigify, and now I'm starting to export it following yet another tutorial.  The thing is, when I was trying to rig the model, I couldn't get the model to go transparent so that I could see the bones inside the model.  Eventually, I managed to get it into wireframe mode, but I can't get it back into solid mode.    It's probably just a display thing and not a property of the model itself, but I want to be sure.  I'm looking at the display options under the "Figure" pane in Blender, and none of the Display check boxes are checked, including the one that says "Wire".  I don't want to import a plain wireframe model into Unity, and even if that doesn't happen, this is functionality of Blender that I should really know anyway, so I'd appreciate any help that anyone has to offer.  If necessary, I can upload the .blend file, but I'm not sure what site people would prefer that I upload it to.