How do I save 4 GB+ files on a FAT32 flash drive?
Getting around the FAT32 4GB file size limit
a) Give a combinatorial proof that for every $n \geq r \geq 1$ that:  $$\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$$  And use (a) to concoct a formula for $1^2 + 2^2 + ... + n^2$ The pdf of $\frac{X_1-\bar{X}}{S}$ Suppose $X_1, X_2,...,X_n$ be i.i.d from $N(\mu,\sigma^2)$ with unknown $\mu \in \mathcal R$ and $\sigma^2&gt;0$  Let $Z=\frac{X_1-\bar{X}}{S},$ S is the standard deviation here.  It is can be shown that  $Z$ has the Lebesgue p.d.f.  $$f(z)=\frac{\sqrt{n} \Gamma\left(\frac{n-1}{2}\right)}{\sqrt{\pi}(n-1)\Gamma\left(\frac{n-2}{2}\right)}\left[1-\frac{nz^2}{(n-1)^2}\right]^{n/2-2}I_{(0,(n-1)/\sqrt{n})}(|Z|)$$  My question is then how to get this pdf?  The question is from  in example 3.3.4  to find the UMVUE of $P(X_1 \le c)$. I can understand the logic and procedures to find the UMVUE but don't know how to get the pdf.  I think this question also relate to this    Thank you very much for help or point to any related references will be also appropriated. Word for low level noise among restless crowd, as sign of confusion or complaint? Dictionary gives me "drone" and "murmur" but I'm not sure if that's the word I am thinking of.  I want to use it to describe a group of people on strike who hear that their demands are not met and the CEO has resigned.  They're not shouting, but they're not whispering either.  They're restless and confused.  I want to say that a certain something (murmur?) was heard among the crowds, to indicate their state. How to make a logo where a letter is made of particles of varying sizes? How can I make a logo in Adobe Illustrator like the AntiParticle logo below, from ?   It is a large number circles of different, varying sizes, which form the shape of a text character. Create an entry in index without creating a Chapter or Section title Why are these pistons pushing? I've lately become hooked into building computers in Minecraft and today I decided to build a giant hard drive. I've built HDDs before, but not at the scale I'm currently attempting, and I anticipated problems. As I was wiring some pistons, they activated and pushed forward oddly. As far as I can tell, there's nothing powering them.    I thought at first that it might be the redstone torches (top left of above pic) but they aren't powered.   Here's a top view of the same pistons. I also thought the line of redstone above  them might be the problem (middle of above pic), but when I destroy it, the pistons stay extended.  Is there a reason why my pistons are extending? If so, is there a way to get them to power (when I want them to) without disturbing the pistons above? General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$. If $k=1$, we have \begin{align} \sum_{n\ge1}\frac{1}{\binom{2n}{n}}&amp;=\frac12\sum_{n\ge1}n\mathrm{B}(n,n)\\ &amp;=\frac12\int _{0}^{1}\sum_{n\ge1}n(t-t^2)^{{n-1}}{\mathrm  d}t\\ &amp;=\frac12\int _{0}^{1}\frac{1}{(t-t^2-1)^2}{\mathrm  d}t\\ &amp;=\frac13+\frac{2\sqrt3\pi}{27} \end{align} I wonder if there exists a general formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$ with $k\in\Bbb N^*$. This may involve some ${}_pF_q$ functions. Can you trade Pokemon from 7th gen (Sun/Moon) to 6th gen (XY, ORAS) and back? Title says it all, I don't see confirmation in  and a cursory google search seemed to say assume no and speculate about the pokemon bank. The following example must be compiled with XeLaTeX to reproduce the issue.  % arara: xelatex \documentclass{article} \usepackage{fontawesome} \begin{document} Text Text \faMobilePhone\ Text Text \end{document}   Normally I am using TeXworks to compile and view the output. With the internal viewer I am getting the desired result. The following image demonstrates it:    However if I open the pdf with Preview (viewer of Mac) the scaling of the icon fails.     If I open the pdf file with Adobe Acrobat Reader the icon is still scaled correctly. If I print the page my printer is also not able to scale the icons correctly.   If I use LuaLaTeX everything seems to work correctly.   Can you reproduce the issue and do you know a solution? I want an editor that is as good as TextPad (for Windows) for compiling and running Java programs on Ubuntu 12.04. Please suggest one. What is the C# equivalent of friend? Possible Duplicate:          I'd like the private member variables of a class to be accessible to a Tester class without exposing them to other classes.   In C++ I'd just declare the Tester class as a friend, how do I do this in C#? Can someone give me an example? In English, especially in a poetic description, ships and cars are  referred to as "she".   Maybe their owners compare their beauty and elegance with those of women, but what if a female owner wanted to describe her yacht or car?   Would she also say, "She is a real beauty", or it might be "he" then?   Does the choice of a pronoun depend on whom she is giving the description of it to — a man or a woman?  What about a man-o’-war or a merchantman? Being ships, are they also referred as "she"?  P.S.  on the use of "she" in reference to ships, but there seems to be no answer to my question there.  P.P.S. My question wasn't pulled out of a thin air. I came across a book by a prominent Russian linguist, G.Veichman, written in 1990, (Novelties in The English Grammar is my translation of the title), where I read that the rule of personification of vehicles may be added regarding a female owner talking about her car using the preposition "he". Period. No further explanation or reference examples. "Oriented" vs. "orientated" Adding/updating field to polygon feature class that lists bordering (neighbor) polygons? I have a dataset of zipcodes.  I want to add a new field "NEIGHBORS" that includes bordering polygons in a comma delimited manner such as attached image: Given a file like this:  1,768,12,46576457,7898 1,123,435,134,146 2,345,6756856,12312,1311 5,234,567465,12341,1341 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212   I would like to list all rows (in bash terminal) such that the value in column 1 appears at least twice (in column 1). The result should be  1,768,12,46576457,7898 1,123,435,134,146 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212 Compare two dates with JavaScript Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes. Proving $\sum_{k=0}^n(-1)^k\binom nk=0$ How do you cite a Github repository? How to use manual partitioning during installation? I'd like to see the full How-To on how to use manual partitioning during Ubuntu installation. The existing guides (at least those I found here) cover only automatic part and leave untouched the manual part (or extremely short and contain no pictures).  I'd like to cover such situations:     If your disk contains other systems: Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$ I have some problems with this exercise. I don't know if it can be done. Consider the polynomial $ x^n - a \in \mathbb{Q} $ Can I compute the Galois group of this over $\mathbb{Q}$? Maybe having a nice "basis.  The splitting field is given by $\mathbb{Q}(\zeta_n,\alpha)$ , where $\zeta_n$ is a primitive root of unity , and $\alpha$ is some number such that $\alpha^n = a $. Well first of all, I want a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different (in this case the computation of the galois group is very simple).  For example one easy case, it's when $a&gt;0$, then $(a)^{\frac{1}{n}} \in \mathbb{R}$ , so clearly the minimal polynomial of $(a)^{\frac{1}{n}} , \zeta_n$ are distincs, and I'm done. If $n$ is odd then , it's also easy, since one root it's also real, for example $x^3-3 $, the real root is $ \root 3 \of { - 3}  =  - \root 3 \of 3  $ , so I can consider the splitting field as $\mathbb{Q}(-\root 3 \of 3 , \zeta_3 )=\mathbb{Q}(\root 3 \of 3 , \zeta_3 )$. The difficult case is when $n$ is even and $a&lt;0$ , for example  $x^8+20$ or $x^4+20$ in some cases as in the second, there are particular cases since there exist algorithms for the Galois group of quartics, but in general. It can be done?  $\underline{Remark}$ I'm searching a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different since in this case the computation of the galois group is very simple.