Does $f_n(x) = x^{1/n}$ converge?
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
Evaluation of Indefinite Integral resulting in Hypergeometric Function I am attempting to derive the result:  $$ \int \left(1+x^n\right)^{-1/m}dx= x\,_2F_1\left(\frac 1m,\frac 1n;1+\frac 1n;-x^n\right)$$  First, I start off with the binomial expansion of the integrand to get:  $$\int\sum_{k=0}^{\infty}\frac{(1/m)_k}{k!}\left(-x^n\right)^kdx  $$  Then, I pull out a $-1$ and interchange summation and integration:  $$\sum_k\int (-1)^k\frac{(1/m)_k}{k!}x^{nk}dx  $$  $$ \sum_k (-1)^k\frac{(1/m)_k}{k!}\frac{x^{nk+1}}{nk+1} $$  $$ x\sum_k \frac{(1/m)_k}{k!}\frac{(-x^n)^k}{nk+1}  $$  So, I'm just right there, but not sure how to express this series in the general form of a hypergeometric series with the two additional Pochhammer symbols.  I even typed this last series into Mathematica, and it returned the Hyper. Function. What am I missing, or how do I transform this last series into the desired form? Vector spaces for the irreducible representations of the Lorentz Group How to Flatten a Multidimensional Array? I have seen this many times, a question is being asked because a previous, duplicate question was asked and answered a few years ago and has no longer relevant answers.  The  is to edit the old question, or add new answers to it, but it is not always happening.  I was wondering, should I still mark it as duplicate and vote to close it? Or just leave it as is? Error: could not start the command in Texmaker when I run makeindex I'm trying to create a nomenclature but I'm getting the following error when I run makeindex:     Error: Could not start the command   This error appears even with this basic example:  \documentclass{article} \usepackage[refpage]{nomencl}  \makenomenclature  \begin{document} Example of nomenclature \nomenclature{A}{Area}  \printnomenclature \end{document}   In the Configure Texmaker editor I wrote: makeindex %.nlo -s nomencl.ist -o %.nls in the makeindex slot. Then I run:   PdfLaTeX MakeIndex   And the error appears... I also tried all suggestions , but nothing seems to work.  I have installed MacTex 2012 distribution, Mac OS X 10.7.5 novel with psi slavery Name the novel, 197x.  Setting is a world of human(oid)s most of whom have the psi ability to enslave weaker others.  (Maybe the word slave and its derivatives are not used.)  Masters and slaves form a tree rather than a dichotomy; everyone delegates as much as they can. The protagonist is an outworlder on a mission, maybe simply doing a survey.  He wears the green robe of a native subculture who lack the power (or maybe they renounce it?) and are immune to it – by law or custom, I think, rather than by nature. His host or primary contact is Jael Forty of Lant, the number being how many slaves he can control; it can fluctuate. How to keep a constant baselineskip when using minipages (or \parboxes)? When a minipage is used to box a text paragraph, the first line of the minipaged text and the last line of the previous text paragraph are closer than two consecutive lines in a standard text paragraph; analogously, the last line of text inside the minipage and the first line of text after the minipage are also closer.  The following MWE illustrates this:  \documentclass{article} \usepackage{lipsum}  \newcommand\Text{Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.\textbullet}  \begin{document}  \Text  \noindent\begin{minipage}{\linewidth} \Text \end{minipage}  \Text  \end{document}   How can I guarantee a constant baseline-skip even if minipages (or \parboxes) are used? I have to do proof of $(a+b)^n$ and $(a+b)^{n+1}$ with mathematical induction.  I finished the first one $(a+b)^n = a^n + na^{n-1}b+\dots+b^n$.  I however have trouble with the second one, I don't know what to start exactly. Any help/hints? How to get the type of T from a member of a generic class or method Let's say I have a generic member in a class or method, like so: public class Foo&lt;T&gt; {     public List&lt;T&gt; Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List&lt;MyTypeObject1&gt;. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar&lt;T&gt;()     {         var baz = new List&lt;T&gt;();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it? This is from problem $8$, Chapter II of Rudin's Real and Complex Analysis.  The problem asks for a Borel set $M$ on $R$, such that for any interval $I$, $M \cap I$ has measure greater than $0$ and less than $m(I)$.  I was thinking of taking the Cantor approach: taking $R$ to be the union of $[a,b]$ with $a$ and $b$ rationals, and for each $[a,b]$ we construct Cantor sets inside it. During theconstruction of each Cantor set, in order to have positive measure on it, we need to take off smaller and smaller intervals from it, namely the proportion goes to $0$. As a result, these Cantor sets are extremely "dense" on their ends. If for an interval $I$ it intersects with the Cantor set on $[a,b]$ while $b-a&gt;&gt;m(I)$, we shall expect the measure of intersection to be rather close to $m(I)$ and then we lose control on these cases.  Is there any way to fix this or shall I consider other approaches?  Thank you The problem Comments are terrible; no one agrees on what they're for, or how long they should be kept. Comment flags are equally terrible, because if no one's on the same page as far as what should be posted in the first place then no one can agree on what should be removed either. On top of that, we have this confusing set of flags where two mean &quot;noise&quot;, one means &quot;vile&quot;, one means &quot;moderator, help!&quot; and one means nothing at all - the end result is that it's all but impossible to even analyze comment flagging. The solution (or, part of it) Two years ago, in a fit of rage, I . Nothing got done. As always, everyone has a different idea of how things are supposed to work, and I'd bitten off more than I could chew. So, here we are, two years later, and comment flags still suck. So let's start by just cutting the fat: if we can trim down the list of flags to a set of clearly distinct problems, we might have something we can build on. Here's what I'm proposing, based on the past two years of discussion:   Re-word the &quot;rude or offensive&quot; flag to read,  rude or abusive: this comment violates .   Remove the &quot;not constructive&quot;, &quot;obsolete&quot; and &quot;too chatty&quot; flags.  Add a new comment flag:  no longer needed: this comment is obsolete, chatty or otherwise unnecessary   Re-word the &quot;other...&quot; flag:  in need of moderator attention: these comments require action by a moderator. Be specific and detailed!    That's it; that's all I'm proposing to start out - simplify things so that we have something to build on. See also: What is object serialization? Bypass BIOS password set by faulty Toshiba firmware on Satellite A55-S1065 laptop? Union of uncountable cardinals I get a "serious errors while checking the disk drives for /boot" error while booting I have just set up my new system by creating three partitions on a whole hard disk (/boot, /home, swap and /). I saw  article and now I am getting those errors and the system provide me with some options: (I to ignore, S to skip mounting or M for manual recovery).   I am forced to choose skip mounting because I don't know what manual recovery is. Despite the error I get I think that the system boots okay because I can use the system but this error is very annoying. The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC. Why couldn't River Song's memories bring back The Doctor in the rebooted universe? In the season 5 finale of Doctor Who, in the wedding ceremony of Amy, River Song showed up outside the door. Moments later, we discovered that she gifted Amy her blank diary which was supposed to contain information about The Doctor. It means River Song remembered The Doctor.  Memories of The Doctor was able to bring The Doctor back to existence in the rebooted Spacetime. Why couldn't River Song's memories work? Short Story: Army investigates barrier and house I am trying to identify the author and title of a short story with the following plot.  A scientist narrates a story where s/he is called in to help the army investigate an unexplained phenomena.  The army has cordoned off an area where a prairie home has appeared. It is surrounded by a dome that allows things to enter but not to leave. Briefing the scientist, the Army explains that it appears that it is a family of five with mother, father, son, daughter, and grandfather. They look completely normal and live an idyllic life of the 40s or 50s.  They continue to send probes in to investigate the dome and its proprieties. Not sure if this a time anomaly or another dimension.  An Army lieutenant, so enamored by their life runs through the barrier to join the family. The Family faces split into an unnaturally wide smile full of sharp teeth runs towards him and tears him to pieces &amp; eats him. The grandfather then looks up acts as if he can see the forces gathered outside the barrier. He then retrieves a book and it looks as if he reads it out loud and the house and barrier disappear. The narrator worries that the aliens will return. Using beamer \visible command inside a table, without adding vertical space When using the beamer \visible command inside a tabular environment, beamer adds an extra vertical space before the text. For example, in the following code, beamer adds an empty line before the word World in the second row. Can this be avoided?  \documentclass{beamer} \begin{document} \begin{frame}   \begin{tabular}{|p{1cm}|p{1cm}|}     \hline     1 &amp; Hello World \\     \hline     2 &amp; \visible&lt;2-&gt;{Hello World} \\     \hline   \end{tabular} \end{frame} \end{document} Mac OS X Darwin: how to reset admin password? Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password?