Binomial expansion of $(x_{1}+x_{2}+...........+x_{k})^{n} $
how many terms will there be once you collect terms with equal monomials? What is the sum of all the coefficients?
Why didn't anybody Summon the Triwizard cup in the maze? We know that the Triwizard cup itself was Summonable. After all, Harry did Summon it in the graveyard.  So why didn't any of the contestants Summon it while in the maze?  Canonical answers, please. Allowing line break at ',' in inline math mode? In the inline math mode ($...$), if the formula is too long, LaTeX will try to break it on operators, e.g.  very long text followed by a very long equation like $a+b+c+d+e+f+g+h+i+j+k+l$ etc   may be rendered as  very long text followed by a very long equation like a+b+c+d+e+f+g+h+i+ j+k+l etc   However, the break won't happen if they are separated by commas, e.g.  very long text followed by a very long equation like $a,b,c,d,e,f,g,h,i,j,k,l$ etc   will overflow the page like  very long text followed by a very long equation like a,b,c,d,e,f,g,h,i,j,k,l etc   How to make LaTeX able to insert line breaks after a comma too? Can Windows use a Linux shell instead of cmd? I was wondering if it is somehow technologically possible for Windows to add some sort of Linux interface?  I think it would win over many programmers to develop on Windows.  Any ideas on this? How to cross-reference an inequality with \cref? I have inequalities being cross-referenced by \cref as equations.  1-) How can I change that? (and still have inequalities with the same numbering as equations)  2-) How can I change that and have inequalities with their own numbering?  \documentclass[12pt]{article} \usepackage{amsmath} \usepackage{cleveref} \usepackage[letterpaper]{geometry} \begin{document}  \begin{flalign} &amp;f(x) \geq g(x)&amp; \label{i:positivity} \end{flalign}  Admitting that \cref{i:positivity} has a solution, ...    \end{document} Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$  I can use the sandwich principle, certain convergence criteria, Cesaro mean theorem, limit arithmetic.. things around this area.  Any help would be greatly appreciated, thanks!  Sorry for not elaborating more at the beginning, rookie first-post mistake I suppose. :) Paradox of General Comprehension in Set Theory, other than Russell's Paradox As is well known, the General Set Comprehension Principle (any class is a set) leads to the Russell Paradox (the class $x \notin x$ cannot be a set). As a result, set theories must restrict the Comprehension Principle to avoid self-reference. For example, in the case of ZFC, this is done by enumerating a small list of "safe" comprehension schema such as Separation.  Does General Comprehension lead to other types of paradox than Russell's? Or is this basically the only thing that can go wrong? Why I can't scan the WhatsApp QR? Why can't helicopters reach mount everest? How to use GCC 4.7 in place of 4.6? So I'm working on a project and I wanted to use some C11 features for C. To use those features GCC 4.7 is required, so I went to synaptic and looked up 4.7, and I found the packages gcc-4.7-base so I installed it[1].   So now that gcc-4.7-base is installed I expected to be able to use 4.7, but no, when I do gcc --version it still shows 4.6.3 even more, when I try to directly call 4.7(via /usr/bin/gcc-4.7) it doesn't exist, though a gcc-4.6 executable does exist.  How do I "activate" GCC 4.7? I read , you do some crazy stuff with update-alternatives, but it doesn't work for me as the gcc-4.7 executable doesn't actually exist on my machine.   Notes: 1. I also saw gcc-4.6-base, so I figured I'd uninstall it, but synaptic attempted to remove every package I had installed and install a Java runtime, so for obvious reason I decided not to remove it. JavaScript post request like a form submit Why do some font commands behave differently? I've always been confused by the differences in behavior of font commands.  For example, we have \mathrm{} and \texttt{}, which can be used like this: \texttt{hello} world.  And then we have \it and \bf which must be used as {\it hello} world. If one uses \it{hello} world, both words are italicized.  Internally, what is the difference here? And was this difference a conscious design decision? If so, why? There is a restriction on setting your birthday:     Oops! There was a problem updating your profile:   - Birthday must be after 1920/01/01   I realize the number of 90 year old users is small, but shouldn't the restriction be a bit more relaxed, such as larger than any ?  Either 120 or 150 seems appropriate.  For example, my grandfather turns 90 next year (and just barely misses the current cutoff), but I can't imagine he's the only one around that age who is computer literate and still active enough to be interested in (the increasingly broad range of) SE sites.  I don't think he has contributed yet (mostly because of the comment restriction, I'd see him commenting before asking or answering), but I have emailed him with links that I know he's read.  Incidentally, the error message is wrong: birthday must be after 1919/12/31 and using the next day is accepted. Asks a question; never responds to answers/comments What do we call someone who asks a question and never responds to answers/comments?    Think of it more as "a pattern of behavior" (somebody who has asked many questions and never responded). I had unresponsive in mind, but that doesn't say that they asked in the first place. bash: warning: shell level (1000) too high, resetting to 1 Pokemon Go Supported Devices Is it possible to query the content of the Time-based Workflow Queue from an Apex unit test to assess that a specific Workflow Rule has been executed and added a new item to the queue? I didn't see anything alike in the documentation, but wish it could be possible to improve testing and stability overtime.  Thanks I'm getting these errors ramdomly, and I don't know if its normal or not.   [39441.061856] ata3.00: failed to read SCR 1 (Emask=0x40) [39441.061866] ata3.01: failed to read SCR 1 (Emask=0x40) [39441.061892] ata3.15: exception Emask 0x10 SAct 0x0 SErr 0x280100 action 0x6 frozen [39441.061897] ata3.15: irq_stat 0x08000000, interface fatal error [39441.061904] ata3.15: SError: { UnrecovData 10B8B BadCRC } [39441.061910] ata3.00: exception Emask 0x100 SAct 0x0 SErr 0x0 action 0x6 frozen [39441.061917] ata3.01: exception Emask 0x100 SAct 0xe SErr 0x0 action 0x6 frozen [39441.061923] ata3.01: failed command: READ FPDMA QUEUED [39441.061933] ata3.01: cmd 60/a8:08:b0:48:62/00:00:00:00:00/40 tag 1 ncq 86016 in [39441.061940] ata3.01: status: { DRDY } [39441.061944] ata3.01: failed command: READ FPDMA QUEUED [39441.061953] ata3.01: cmd 60/a8:10:b0:49:62/00:00:00:00:00/40 tag 2 ncq 86016 in [39441.061959] ata3.01: status: { DRDY } [39441.061963] ata3.01: failed command: READ FPDMA QUEUED [39441.061972] ata3.01: cmd 60/58:18:58:4a:62/00:00:00:00:00/40 tag 3 ncq 45056 in [39441.061978] ata3.01: status: { DRDY } [39441.061987] ata3.15: hard resetting link [39441.608302] ata3.15: SATA link up 3.0 Gbps (SStatus 123 SControl 300) [39441.609090] ata3.00: hard resetting link [39441.929246] ata3.00: SATA link up 3.0 Gbps (SStatus 123 SControl 320) [39441.929333] ata3.01: hard resetting link [39442.249184] ata3.01: SATA link up 3.0 Gbps (SStatus 123 SControl 320) [39442.263242] ata3.00: configured for UDMA/133 [39442.277570] ata3.01: configured for UDMA/133 [39442.277725] ata3: EH complete   I'm also pasting smartctl -a for ,  and .  Thanks in advance for your help. What will Sony do if someone uses my account as primary on another ps4 without my knowledge? What will Sony do if someone uses my account as primary on another ps4 without my knowledge? Will the account be banned? Or will the other guy that has my account as primary be banned? After how long? I have no credit card on my account so I don't care too much but I want to know.   He uses my account on his ps4 as a primary account. I think to use my digital games as free (Sharing, but without my knowledge). How to make sure that Thinkpad discharges external slice battery first? The thing is that when an external slice battery pack is connected, the laptop first discharges the internal one. This is a problem because then it is impossible to switch between multiple external battery packs without powering off the laptop. It is also not possible to just disconnect the external battery pack when you e.g. need to insert it into a docking station.  Thus, my question: how to change the discharge order under Linux?  For my use cases following order would make much more sense: when an external slice battery is connected, first discharge it completely before using power from the internal battery.  Background: For some Thinkpad models (e.g. X220) there are slice battery packs () available that you can connect to the bottom of the laptop (similar to a docking station).  They seem to be supported well on Linux - e.g. the Gnome Shell battery applet includes both batteries (internal and external) when connected - including displaying the current capacity for each. "Always on top" option missing for Firefox/Chrome in 18.04