Is there any way I can intuitively demonstrate or remember the formula listed at  for the Pascal triangle?  I'm talking of  $$ {n\choose k}= {n\choose k-1}\times \frac{n+1-k}{k} $$  I tried with a piece of paper and it definitely works.. but I don't know why. There is no proof or demonstration.. so: why does it work?
I've found in Wikipedia the formula for calculating an individual row in Pascal's Triangle: $$v_c = v_{c-1}\left(\frac{r-c}{c}\right).$$ where $r = \mathrm{row}+1$, $c$ is the column starting from $0$ on left and $v_0 = 1$.  Now, I've tried to do by hand and it works,  but I don't understand how to find this magic formula when I don't have access to Wikipedia...:)
Within 300 km of Tokyo: Where for flora, landscape, nature? Create element in pdf that doesn't print to paper Here's a module with castellated pads attached to an eval board:  (source: ) Looking closely at the wires interfacing with the castellated pads, they're clearly soldered to the eval board. However, they don't look like they're soldered to the module, but rather they're being pressed against the pads with the tension in the wire. It also looks like the free end of the loops are protruding down into a channel cut in the PCB. Do these kind of connectors/metal loops have a name? Does moving leave the object in a usable state? Why should the Standard Model be renormalizable? Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These theories are valid until a scale $\Lambda$ (ultraviolet cutoff), after this scale an effective theory need a UV completion, a more "general" theory.  The Standard Model, as an effective theory of particle physics, needs a more general theory that addresses the phenomena beyond the Standard Model (an UV completion?). So, why should the Standard Model be renormalizable? A user has asked  which did not receive much attention, and thus the user deleted the post. After some time, the user asked the  (with just slight changes to the title and a tag change), so that it could receive a bit more attention. The strange thing is that the question was not downvoted or poorly written, and yet the user deleted the original post. Now, since the original question was deleted, I could not mark the new one as a duplicate (it threw an error). My question is, how do we handle such questions? Just let them be as such or let the user know about it or is there another way to handle such situations? I've observed several incidents where users inadvertently posted detailed, sensitive information. For example, a Server Fault user who posted a question with working login credentials to his actual production server, or the Stack Overflow user who posted actual medical records as example data for his question.   What should be the procedure for handling such cases? Where can I find computer modern fonts for use in other programs, e.g. Adobe Illustrator? For some complicated diagrams, I need to use something like Adobe Illustrator or Inkscape, and would like to include nicely typeset labels. (I'm aware of post-processing solutions, such as pinlabel.) One way to do this is to use a closely-matching font, and then convert fonts to outlines. Better, however, would be to use Computer Modern directly in Illustrator.  Where can I find a Computer Modern font compatible with Adobe Illustrator? When I installed my SSD I just mounted with discard and didn't sweat it. However today I was reading about the pros and cons of using fstrim instead and decided to run the program to get an idea of how long it would actually take (still with my partitions mounted with discard). The command took several minutes on both my root and home partitions. For my home partition I used -v and got this:  $ sudo fstrim -v /home /home: 137494052864 bytes were trimmed   This is more than the amount of free space on the partition!  $ df -h /home Filesystem      Size  Used Avail Use% Mounted on /dev/sda2       206G   78G  118G  40% /home   Subsequent runs finish in less than a second, eg:  $ sudo fstrim -v /home /home: 0 bytes were trimmed   Surely if I have always had the partition mounted with discard, fstrim should not trim a large amount of data like that? The discard option is definitely enabled, here are the relevant fstab lines:  UUID=xxxxxxxx...    /          ext4   noatime,discard,errors=remount-ro  0      1 UUID=xxxxxxxx...    /home      ext4   noatime,discard,errors=remount-ro  0      2   And mount output lines:  /dev/disk/by-uuid/xxxxxxxx... on / type ext4 (rw,noatime,discard,errors=remount-ro,stripe=128,data=ordered) /dev/sda2 on /home type ext4 (rw,noatime,discard,errors=remount-ro,stripe=128,data=ordered)   The SSD is a TOSHIBA THNSNS256GMCP. Why does this happen? How can you use optional parameters in C#? Note: This question was asked at a time when C# did not yet support optional parameters (i.e. before C# 4).  We're building a web API that's programmatically generated from a C# class. The class has method GetFooBar(int a, int b) and the API has a method GetFooBar taking query params like &amp;a=foo &amp;b=bar.   The classes needs to support optional parameters, which isn't supported in C# the language. What's the best approach? Let's suppose I'm a wizard casting a ranged spell. An enemy is behind cover but I suspect he'll come out, so I ready an action to cast at him when he comes out; but I don't want to risk getting charged at by another enemy and losing concentration or taking disadvantage. Can I say:  "I ready a spell. When that guy over there leaves cover, or when any enemy gets within 5 feet of me, I will cast it on that enemy"? Keyboard shortcut to autocomplete the user in comments In bibliography, how to print the page in my text where I cited certain paper? How to get, for instance,  [19] S. Roth and M. J. Black. Fields of experts: A framework for learning image priors. In IEEE Conf. on Computer Vision and Pattern Recognition, 2005. 1, 2, 7, 8  where the last numbers (1, 2, 7, 8) are the pages where I cited the paper in MY TEXT?  This would be like a reversed reference, or a index for bibliography. Where do I ask where to ask? If I have a specific question I want to ask about, but I don't know which Stack Exchange site would be on topic for asking that question, where can I ask where to ask that question?  Is there any generic place where we can ask for advice? Is it here?  This is not about a specific question but in general.  For example: "Where should I ask for advice about fishing?", or if I need to know where I should ask "What would be the best fishing rod to fish for salmon?" (regardless of how good/bad these examples are) Gravity as a gauge theory Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory).   Why should "classical" gravity be some (non-trivial or "special" or extended) gauge theory? Should quantum gravity be a gauge theory?  Remark: There are some contradictory claims in the literature to this issue. To what extent gravity is "a gauge" theory?Obviously, GR is not a YM theory. So, why do some people say that gravity "IS" a gauge theory? I found this question relevant, e.g., then we handle GR in the Einstein-Cartan theory or any other theory beyond GR, like teleparallel theories or higher-derivative gravitational theories. So I think it could be useful to discuss the "gauge flavor" of gravity here. One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term  \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. Different choices of $\xi$ correspond to different gauges ($\xi=0$ is Landau, $\xi=1$ is Feynman etc.) The propagator for the gauge field is different depending on the choice of gauge. The choice of Landau gauge forces $\partial_\mu A^\mu=0$, but I have never seen a similiar statement for the other gauges. I would like to know what constraint on the gauge field is produced by the other covariant gauges. For instance, what is the constraint on $A_\mu$ when $\xi=1,2,3,...$ etc. Is it still $\partial_\mu A^\mu=0$ or something different (it seems like it should be different)? Are there any examples of subspaces  of $\ell^{2}$ and $\ell^{\infty}$ which are not closed? Bug Identification: Tiny Bugs How to reverse the direction of the y axes Are layer files compatible between ArcGIS 10 and 9.3? If I save layer files in ArcGIS 10, can they be opened and modified in ArcGIS 9.3?