Prove that:  $$(n!)^2&gt;n^n$$  Also prove that, $$2×4×6......(2n)&lt;(n+1)^n$$  I haven't solved any inequalities of this kind before so all suggestions are welcome.
Show that if $n&gt;2$, then $(n!)^2&gt;n^n$.     My work: I tried to apply induction. So, at the induction step, I need to prove, $n^n&gt;(n+1)^{n-1}$ Here, I tried to use induction again without any luck. I also took log of both sides, but I did not get anything. Please help!
A word that says a person is both female and your friend It's often confusing for me to talk about my friends, especially my female friends. This is because in Dutch there are words for both male ("vriend") and female ("vriendin") friends. In English however, there's as far as I know only the word friend, which can mean both a male or a female friend.  For this reason I was wondering if there is a word to say a person is both female and a friend. Why is a nonstop flight sometimes more expensive than multiple connections? Usually I find a flight I like that uses one or more connections with the same or different companies. In these cases, if the distance between the first and the second connection is not too large, I prefer to go by bus or train and then take the flight. The problem is that sometimes it is more expensive to take the flight in the second airport than to take the flight from the first one. I mean, I'm wondering why sometimes it is more expensive to take only a flight than to take the same flight and another one.  A practical example (and real, you can check with SkyScanner). Imagine I am in Madrid (Spain) and would like to go to Rio de Janeiro (Brazil) on April 1st. The cheapest flight I have found is this:     TAM airlines: MAD -> GRU -> GIG : 507 €   Fantastic! GRU is one of São Paulo's airports. That's perfect for me! I'll go on to Rio traveling overland. But then, I look for this flight (MAD -> GRU, non-stop):     TAM airlines: MAD -> GRU : 597 €   It's the same flight, 90 € more expensive! I've found this kind of behavior a lot of times and I'm intrigued to know why it happens. Installing titling.sty onto an offline Windows machine I'm trying to compile a file for which I need titling.sty:  ! LaTeX Error: File `titling.sty` not found.  The two biggest issues are 1) it's on a Windows machine (I'm really only &quot;comfortable&quot; with the Unix command line) and 2) the machine cannot be connected to the internet (so automatic approaches are impossible). Assuming the error means I'm missing a package and following some related advice (e.g., ), I downloaded the file , transferred it to the offline machine, and unzipped it, then tried to run: latex titling.ins  But this gave me an error (given I can't copy-paste, I'm including what I think may be relevant):  ******************************************************** * No Configuration file found, using default settings. * ******************************************************** ! ************************************************** * Could not find your \batchfile=titling.ins. **************************************************. \processbatchFile ...****************************}                                                  \fi \else \ifDefault \Msg ... 1.1092 \process@first@batchfile  I have no idea how to proceed from this. How can I install titling.sty on this machine? Does it make sense to use a date variable in a regression? I'm not used to using variables in the date format in R. I'm just wondering if it is possible to add a date variable as an explanatory variable in a linear regression model. If it's possible, how can we interpret the coefficient? Is it the effect of one day on the outcome variable?   See my  with an example what I'm trying to do. Why does Windows 7 ask for additional drivers when installing from a USB 3.0 drive? biblatex in a nutshell (for beginners) Is there a 'biblatex in a nutshell' guide out there? I'd like if someone explained to me the essentials on how to use biblatex (what lines I have to write in my document, which files I have to have, how many times and what I have to compile), so then I can go to  to customise it further. Propose Newbie-Overflow site or section Because the perl section is looking like that right now. I believe that Stack Overflow is going out of it's charter in becoming a newbie FAQ when as far as the original reasoning it was meant to be something along the lines of an expert site.   is a good example of what I mean in Perl. It probably could be closed because it's a duplicate, or some other reason.   I would also like to indicate that I don't hold back answering newbie questions. It's just when I think of an obscure "stack overflow" error that's beating you some 3 am close to deadline, that's not "Howcum Perl print ..." and follows with something that causes a vast majority of Perl programmers to say oops, because they know exactly what's going on.   So the proposal is   A new site. "Move to Newbieville" A new "section" A new status somewhat similar to Closed ("Newbied") but still can be updated all the same as an open question.   I'm not against giving some newbies an assist, but I feel a FAQ for rank newbieism is not something that SO started out to be, based on the original concept of a Expert Site.   Including comment to Gnoupi:   I said nothing about making newbies unwelcome. Like I said. I answer them--heck, I think I've even answer homework questions. I've answered on the vague impressions that I can glean from posts that have 4 close votes. It can even lead to avoiding downvoting or yelling at newbies by more established curmudgeons if there is a special action you can do to gently inform newbies that this is a real newbie question.  However, you have to know that to some people newbies are already unwelcome. There is a site ethic, but the individual is also going to decide how much they welcome newbies. And people do post RTFM answers already.   Anyway, I'm one vote away from a peer pressure badge it seems. (Nope, nailed it.)    EDIT  For somebody jumping to the conclusion that I'm hostile to newbies:  just earlier Early 80s anthology book about human kind being feared by other races in space I always thought the book was Manifest Destiny but its not. The story that sticks in my head was a human in a cage over a pit? Aliens walk in and discuss how dangerous humans were. He eventually escapes. Man I miss this book. wish I wouldve written down every book I ever read. Ugh Can't use method return value in write context How to hyperlink only the year part when using natbib and hyperref I am using the natbib and hyperref packages:  \usepackage{natbib}  \usepackage[pagebackref=true, plainpages=false, bookmarks, bookmarksnumbered, colorlinks, linktocpage=true, linkcolor=blue, citecolor=blue, filecolor=black, urlcolor=blue]{hyperref}   With my current settings (above) both the name and the year are hyperlinked.  My question is, whether there is a way to hyperlink (or color) only the year-not the author(s).   I have the impression reading this post  that biblatex does it by default. However changing to biblatex is not an option for me at this point.  Any helpful comments will be greatly appreciated. What is the difference between linear regression and logistic regression? How do I display a decimal value to 2 decimal places? Is there a software utility to adjust screen gamma/brightness/contrast? When conducting multiple regression, when should you center your predictor variables & when should you standardize them? Strange result when removing item from a list while iterating over it On duplicate questions, I often see different headings for the duplicate question list. These include:     Possible Duplicate:    [duplicate question list]   and      This question already has an answer here:    [duplicate question list]   and more recently,     This question is an exact duplicate of:    [duplicate question list]   What decides which heading is placed before the duplicate question list? Which one is correct to say: "It's me" or "It's I"? "Parsing filters unsupported" error during extraction of RAR file I have received an .rar which I wish to unpack as it contains something rather important to me that I need to really have now. However even though I can view the contents of the .rar archive in the Archive Manager, I am unable to extract it due to this error:    The archive should contain two folders within it, each though contain at least 10 audio files as well as a PDF file each (I don't know what the contents exactly should be except for there should be audio files in there, and the content I have described is what I can see from the Archive Manager's view). So the only thing I am left with except the error is one of the folders and one of the audio files, but it says it has 0 bytes in it.  So how exactly do I fix this problem? I am running Ubuntu GNOME 16.04.1 with GNOME 3.20.  Information Update:  In reply to a comment requesting the output from the dpkg -l unrar unrar-free command:  Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name           Version      Architecture Description +++-==============-============-============-================================= un  unrar          &lt;none&gt;       &lt;none&gt;       (no description available) dpkg-query: no packages found matching unrar-free Why can't I log into minecraft with a mojang account? I created a Mojang account and downloaded the Minecraft launcher, but when I started it up, I couldn't log in. Since the log in fields did not require a username, I tried typing in my email, and still couldn't log in. I've tried after resetting my password, but that didn't work either. What am I supposed to do to log in and play? Does "Going Infinite" necessarily end the game?