Evaluate $ \lim_{n\to+\infty}\frac{1}{n}\sum_{k=1}^n\Big[\frac{2n}{k}\Big]-2\Big[\frac{n}{k}\Big]$.
Limit of Series with differences of Floor function
Display Custom Fields in a SharePoint 2010 Content Query Web Part Using SharePoint 2010, Having Custom List With 4 Columns, Now I am Using Content Query Web-part To Display List Data ,But Currently It Display Only First Column, SO How to Display Custom Fields in a SharePoint 2010 Content By Query Web Part Modular arithmetic problem (mod $13$) $$\large2017^{(2020^{2015})} \pmod{13}$$  I am practicing for my exam and I can solve almost all problem, but this type of problem is very hard to me. In this case, I have to compute this by modulo $13$. When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016). I have done major updates to my website, and renamed all my URLs.  How can I tell Google that I have renamed these URLs and let Google refresh its index?  My website URL: http://www.pndmasr.com/  My sitemap: http://www.pndmasr.com/sitemap.xml  I have uploaded my sitemap via Google Webmaster Tools many times.  However, every time I search Google for "pndmasr", I still get results with old pages. I have waited more than 3 days but the problem remains. Any suggestions?  Is there a problem with my sitemap? With biblatex, is it possible to replace one author of an author list by a bibnamedash or idem string? With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work. Is there a simple way to explain how Kepler's third law follows from the inverse square law that of gravity  (and laws of motion)  For example for Kepler's second law we can say it's because Gravity is a central force  What is it about the law of gravity which ultimately gives rise to Kepler's third law? Are collective nouns always plural, or are certain ones singular? I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved? How do you find the transfer function of a controller? Below is a block diagram of the system. I thought the circle symbol with the plus and minus sign was an op-amp but I'm not sure whether that's the case. I want to find the closed loop transfer function. If there was no feedback (open loop), then I think I could find the output as Y(s) = Vin*G. This would mean that the transfer function is Y(s)/Vin = G.  Any ideas for how to find the closed loop transfer function and what the circle means? If one is asking for a person, what should s/he say&mdash;1 or 2?   Could I speak to Kristina? Could I speak with Kristina? I am looking for a quick way to sleep without closing the lid, or using the mouse.  If it matters, I have Lion version OS and a MacBook Air. If $G$ is a compact topological group, how to show that a finite index subgroup of $G$ is open ? I really don't know where/how to start...  PS : I precise that by "compact" I mean that it is hausdorff and that any recovering of $G$ by open sets has a finite sub-recovering (sorry if I wasn't unclear) Prove if $\operatorname{ord}(a)=m$, $\operatorname{ord}(b)=n$, and $\operatorname{gcd}(m,n)=1$, then $\operatorname{ord}(ab)=mn$.   I was reading this and was thinking how this proof would look like. I tried to do it and am not sure if this is correct. Here is what I did:  If $a$ and $b$ commute then $(ab)^{mn} = a^{mn} * b^{mn} = (a^m)^n * (b^n)^m = 1 * 1 = 1.$ So $ord(ab) | mn$.  Now, take $k = \operatorname{ord}(ab) = m^\prime * n^\prime$ where m' is relatively prime with $n$ and $n'$ is relatively prime with $m$. By the result above $m' | m$ and $n' | n$. Now we have $((ab)^k)^{m/m'} = 1$ since $(ab)^k=1$. But on the other hand, by the commutativity:  $$((ab)^k)^(m/m') =$$  $$((ab)^(m' * n'))^(m/m') =$$  $$ a^{n'm} * b^{n'm} = $$  $$(a^m)^{n'} * b^{n'm'}=$$  $$b^{n'm'} = 1$$  This implies that $n' * m'$ is divisible by $n$. But $m'$ is relatively prime with $n$, so we must have $n' = n.$ By symmetry, $m' = m$. So $ord(ab) = mn$.  Just to say this again, I want to prove if $a$ and $b$ commute and $m$ and $n$ are relatively prime then   $$ord(ab)=mn.$$   The comments are vague. I guess this must be the answer then and there probably is not another way to do this. Script to remove certain span elements from an HTML file How to find solutions of linear Diophantine ax + by = c? Where Android apps store data? Could you list all possible directories where Android apps may store data, providing description what kind of data are stored in each directory? Why is a home fiber connection asymmetric? I recently switched from an ADSL to a fiber connection and was surprised to see that the bandwidth is asymmetric (1 Gbps down / 250 Mbps up).  While this is understandable in ADSL, I do not understand why fiber at home is asymmetric as well? It is not a limitation of the technology (I have symmetric fiber at the office, and always had) How does Cypher exit/enter the Matrix without an operator? How can I let a footnote continue on the next page? I have a rather long footnote which breaks a listing in two parts, unnecessarily.  Since the listing is more important then the footnote I'd rather lake to have the footnote split.   Can I customize (one or all) footnotes to have a maximal length before they are continued on the next page? Or can I manually split a footnote in two to get the effect? Although the merits of stepwise model selection has been discussed previously, it is becoming unclear to me what exactly is "stepwise model selection" or "stepwise regression". I thought I understood it, but not so sure anymore.  My understanding is that these two terms are synonymous (at least in a regression context), and that they refer to the selection of the best set of predictor variables in an "optimal" or "best" model, given the data. (You can find the Wikipedia page , and another potentially useful overview .)    Based on several previous threads (for example here: ), it appears that stepwise model selection is considered a cardinal sin. And yet, it seems to be used all the time, including by what seem to be well respected statisticians. Or am I mixing up the terminology?  My main questions are:   By "stepwise model selection" or "stepwise regression", do we mean: A) doing sequential hypothesis testing such as likelihood ratio tests or looking at p-values? (There is a related post here: ) Is this what is meant by it and why it is bad? Or B) do we also consider selection based on AIC (or similar information criterion) to be equally bad? From the answer at , it appears that this too is criticized. On the other hand, Whittingham et al. (2006; )1 seems to suggest that variable selection based on information-theoretic (IT) approach is different from stepwise selection (and seems to be a valid approach)...?  And this is the source of all my confusion.  To follow up, if AIC based selection does fall under "stepwise" and is considered inappropriate, then here are additional questions: If this approach is wrong, why is it taught in textbooks, university courses, etc.? Is all that plain wrong? What are good alternatives for selecting which variables should remain in the model? I have come across recommendations to use cross-validation and training-test datasets, and LASSO.   I think everyone can agree that indiscriminately throwing all possible variables into a model and then doing stepwise selection is problematic. Of course, some sane judgement should guide what goes in initially. But what if we already start with a limited number of possible predictor variables based on some (say biological) knowledge, and all these predictors may well be explaining our response? Would this approach of model selection still be flawed? I also acknowledge that selection of the "best" model might not be appropriate if AIC values among different models are very similar (and multi-model inference may be applied in such cases). But is the underlying issue of using AIC-based stepwise selection still problematic?  If we are looking to see which variables seem to explain the response and in what way, why is  this approach wrong, since we know "all models are wrong, but some are useful"?   1. Whittingham, M.J., Stephens, P.A., Bradbury, R.B., &amp; Freckleton, R.P. (2006). Why do we still use stepwise modelling in ecology and behaviour? Journal of Animal Ecology, 75, pp. 1182–1189. Repeat the same reference in footnote on different pages