Sum of infinite telescoping series $\sum_{r=2}^\infty \frac{1}{r^2-1}$?
find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
How do I technobabble without sounding like technobabble? On occasion, I've had reason to describe obviously fictional technical processes in-character. I'd like to be able to describe on these occasions without sounding like I'm saying utter gibberish. But it's not straightforward to do, particularly if I have to make stuff up on the spot.   How do I do it? Is normal extension of normal extension always normal? How can I find the number of partitions of $n$ into exactly $k$ distinct parts, where each part is at most $M$?  The number of partitions $p_k(\leq M,n)$ of $n$ into at most $k$ parts, each of size at most $M$, is given by the generating function: $$  \binom{M+k}{k}_{x} = \prod_{j=1}^{k}\frac{1-x^{M+k-j+1}}{1-x^j}= \sum_{n=0}^{kM} p_{k}(\leq M,n) x^n $$  For the number of the partitions $p_k(\mathcal{D},n)$ of $n$ into at most $k$ parts there is the recurrence relationship: $$   p_{k}(\mathcal{D},n) = p_{k}(\mathcal{D},n-k) + p_{k-1}(\mathcal{D},n) $$  But what, if I want to count only the partitions with distinct parts and restricted number of parts and restricted part size?  Update: Now I know the generating function for the number of distinct restricted partitions $p_k(\leq M, \mathcal{D},n)$ of $n$ into exactly $k$ distinct parts, all at most $M$ is $$    \prod_{j=1}^{M} (1+xq^{j}) = \sum_{k,n=0}^{\infty}p_k(\leq M, \mathcal{D},n)x^{k}q^{n} $$ and there is also a recurrence relation $$    p_k(\leq M, \mathcal{D},n) =         p_{k-1}(\leq M-1, \mathcal{D},n-k) +         p_k(\leq M-1, \mathcal{D},n-k) $$ How can I prove this? Could you recommend a book, where I could read about this? What are preimage resistance and collision resistance, and how can the lack thereof be exploited? What is "preimage resistance", and how can the lack thereof be exploited? How is this different from collision resistance, and are there any known preimage attacks that would be considered feasible? Why don't files from Xbox 360 show up when USB drive is plugged into computer? I'm using a Lexar JumpDrive S73 32GB USB flash drive. I've configured it on my Xbox 360 and got a message saying it's compatible and meets the standards, but when I plug in it in my computer no files show up, even in Horizon.   After the driver was installed, both the USB mass storage and Lexar JumpDrive USB device were ready to use (installed properly), but it said no driver found for Xbox 360.    I tried looking for some sort of driver (which sounds silly) but I couldn't find anything.  I'm attempting to mod Minecraft on my Xbox and I don't want to buy another USB. Is there an (easy) way to create or personalize .bst files? When you prepare an article for a journal (in my case, Quantum Information and Computation, Rinton Press), often they ask you to use some format for your references; in my case, the following:     [1] R. Calderbank and P. Shor (1996), Good quantum error          correcting codes exist,  Phys. Rev. A, 54, pp. 1098-1106.      [2] M.A. Nielsen and J. Kempe (2001), Separable states   are  more disordered globally than locally, quant-ph/0105090.      [3] A.W. Marshall and I. Olkin (1979), Inequalities:   theory of majorization and its applications, Academic Press (New   York).   The issue is, sometimes (and this is the case) they do not provide a .bst style file for bibtex users. I (and I guess many other people) prefer not to copy all the references of a bibtex file one by one into a tex document. So here is the question I am trying to answer:     What is the easiest way to create a .bst file? (for Rinton or any other publisher)   At first sight, I thought this would be very easy to do: after all, a .bst file is just a mere script to give format to a list. Strangely to me, after a long search I have been unable to find a simple clean solution to this problem. These are the the options I have been looking at:   I have tried to adapt a previous .bst file: concretely, apsrev4-1.bst, which has a similar format. Other people have tried this solution before , . However, it is an ugly option. First, it requires going through the script of the .bst and understanding it. Second, the script format used in different .bst files differs (quite annoyingly), so it is not easy to modify them unless you do understand what's written. The above solution is quite hideous and you really lose time on it, so I was wondering: isn't there any software tool (hopefully with a GUI) that does this job? It should, after all, pretty easy to program for a .bst script expert some sort of program to generate .bst files. There are some related questions in this site asking for something similar , ; there I have seen a couple of proposed apps, but going through their manuals they seem not so easy to use. Isn't there some software tool available to generate a .bst in less than 1 hour of work?   Remarks: ideally I would like to use/personalize/create .bst styles that support eprint fields (e.g. aps4-1.bst). Error when using TikZ-Feynman package Today I downloaded and installed the new  package to draw Feynman diagrams. I included the packages   \usepackage{tikz}  \usepackage{tikz-feynman} \tikzfeynmanset{compat=1.0.0} \usetikzlibrary{shapes,arrows,positioning,automata,backgrounds,calc,er,patterns}   into my preamble (changed them already many times).  However, already a simple sample code like  \begin{tikzpicture} \begin{feynman} \vertex (a) {\(\mu^{-}\)}; \vertex [right=of a] (b); \vertex [above right=of b] (f1) {\(\nu_{\mu}\)}; \vertex [below right=of b] (c); \vertex [above right=of c] (f2) {\(\overline \nu_{e}\)}; \vertex [below right=of c] (f3) {\(e^{-}\)}; \diagram* { (a) -- [fermion] (b) -- [fermion] (f1), (b) -- [boson, edge label'=\(W^{-}\)] (c), (c) -- [anti fermion] (f2), (c) -- [fermion] (f3), }; \end{feynman} \end{tikzpicture}   directly gives the error:     Package pgfkeys Error: I do not know the key '/graph drawing/node distance'.   Can you please help me? 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I was considering purchasing Family Tree Maker only to find it has been discontinued.    What do they plan for a replacement ? It is said one should avoid staring at Sun as it can damage the eyes, but it is also said that one should not come out in sun during eclipse as it emits dangerous rays. Is that true? If yes, why?