If we know that $\frac{2^n}{n!}&gt;0$ for every $n\in \mathbb{N}$ and $$\frac{2^n}{n!}=\frac{2}{1}\frac{2}{2}...\frac{2}{n}$$ how to bound this sequence above?
Why is     $$\lim_{n \to \infty} \frac{2^n}{n!}=0\text{ ?}$$   Can we generalize it to any exponent $x \in \Bbb R$? This is to say, is     $$\lim_{n \to \infty} \frac{x^n}{n!}=0\text{ ?}$$     This is being repurposed in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: .
Is the "Final Release" a "Development Release"? Update  appear to have been updated recently (as of writing this the last update appears to have taken place on 3rd of June) to include the following statement:  The -d switch is necessary to upgrade from Ubuntu 18.04 LTS as upgrades have not yet been enabled and will only be enabled after the first point release of 20.04 LTS.  Also note that .  TLDR (as of 15 Aug 2020):   is the canonical tracking document for the first Focal Fossa point-release (20.04.1). It’s a live document. The Ubuntu release team will be updating it as we work on releasing 20.04.1. […] Upgrades from 18.04 to 20.04.1 are still disabled as we are working through a few upgrade blockers   Edit The answers (so far) do not answer the question. The question is pretty simple. Ubuntu.com points to a &quot;FinalRelease&quot;, which turns out to be a &quot;Development Release&quot;, see evidence below. I'm not asking how and when to upgrade. I'm pointing out what seems to me to be an apparent inconcistency (in semantics, linguistics, logic) in the way Ubuntu names or labels its releases. From an answer to the question I'd except someone to pick up and acknowledge this inconsistency. An answer could start with a &quot;Yes, ...&quot; or a &quot;No, ...&quot;, for starters. (Moreover, a good answer could distinguish between the release being in dev stage and/or the upgrade process (e.g. from LTS to LTS) being in dev stage, if appropriate.) This question, as I see it, is not a duplicate. Futher, I think it is a question which deserves a non-patronizing answer. Thanks.   indicates that today (23rd April 2020) the new Ubuntu 20.04 LTS is to be released.  See &quot;condensed screenshot&quot; here:  Indeed, it seems that that's what happened, see  and :  However, when following the instructions to upgrade (from 18.04 LTS to 20.04 LTS) found  and elsewhere (edit: actually , too!), even prior to the July point release, I'm a bit confused to see that the instruction is to use update-manager -d which also points to the &quot;Development Release&quot; (see screenshot below) rather than the &quot;FinalRelease&quot; (see screenshot and link above). Is the &quot;Final Release&quot; (which I'm after) the/a &quot;Development Release&quot;? Why isn't it called something like &quot;Production Release&quot; or &quot;Final Release&quot;? When will it no longer be referred to as &quot;Development Release&quot;? In July? I'm confused :( Why NuGet adds app.config with assemblyBinding to LIBRARY projects during a NuGet package update? How to extract and install .deb without the command dpkg? I am running Debian jessie stable in order to understand how the .deb package interacts with the system. What is the correct way to extract and install a packge_name.deb without the command dpkg? How can you dynamically create variables via a while loop? Will having multiple domains improve my seo? How to upload a file of size 2GB from Apex? Is there any sobject that I can make use of? show that a distance function is continuous What TV movie had lost space cadets who piloted yellow tripod robots, and a squid bad guy? I'm trying to find a movie I watched on TV, probably in the 90s. I think it was a made-for-TV movie.  It was about a ship with an AI. The ship was crewed by young adults. I think they were cadets?   There was an accident (like a warp drive malfunction) and they end up in another part of space where they meet a female alien whose ship had been shot down.  I remember they had manned robots they would pilot and they took them to a planet to get upgraded and they are attacked by more manned robots. They had three legs and they were yellow, I think.  I also remember the baddie had a holo-projector or something like that which allowed him to change his appearance. He commanded a massive fleet and he worked for someone he spoke to in a video chat that looked like a squid. Rounded caps on a Bezier Curve pipe This may be a simple question.  Essentially I am procedurally generating random 3D figures using a bezier curve and bezier circle bevel object, however, one of the only things I can't figure out how to do is how to round the end caps of the object.   I have tried using a taper object like suggested  but have had only limited success.  This is about as close as I've gotten:   I should note that all of this is done through Python and I'm not modeling any of this by hand. So any suggestions for how I can make the rounded caps programmatically would be greatly appreciated. How to make program autostart only in GNOME I use both GNOME and KDE SC. In GNOME, I use Docky but I do not use it with KDE. So, I would like Docky to start up only when I login into GNOME not KDE. In KDE, there is an option to make a program autostart only in KDE. But I cannot find any such option in GNOME.    How can I do this?    Thanks in advance. datetime conversion to CDT Can anyone please help me how to convert the given time into CST timezone.  Input timezone will change dynamically, so i want to convert the given timzone into CST and then need to get the hour from that CST timezone in apex. In the construction of types of numbers, we have the following sequence:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$  or:  $$2^0 \mathrm{-ions} \subset 2^1 \mathrm{-ions} \subset 2^2 \mathrm{-ions} \subset 2^3 \mathrm{-ions} \subset 2^4 \mathrm{-ions} $$  or:  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions"  With the following "properties":   From $\mathbb{R}$ to $\mathbb{C}$ you gain "algebraic-closure"-ness (but you throw away ordering). From $\mathbb{C}$ to $\mathbb{H}$ we throw away commutativity. From $\mathbb{H}$ to $\mathbb{O}$ we throw away associativity. From $\mathbb{O}$ to $\mathbb{S}$ we throw away multiplicative normedness.   The question is, what lies on the right side of $\mathbb{S}$, and what do you lose when you go from $\mathbb{S}$ to one of these objects ? How can I do traffic shaping in Linux by IP? We have a transparent proxy setup. I tried looking for traffic shaping in Linux, and all I could find online was to limit traffic by interface (eth0/eth1...).  I need to limit the bandwidth (never exceeding a specific limit) by IP address or IP ranges and I can't find a way to do that.  Is there any way to do that? How can I determine whether a 2D Point is within a Polygon? Fantasy novel with amnesiac witch, impotent soldier and cursed animals The story is set in a vaguely medieval world in which a young woman has been cursed by the evil witch who has enslaved her and caused her to lose her memory. With the aid of her talking animal friends who have also been cursed (toad has a huge stone under his tongue meaning he can't feed and a crow with a gem embedded in its wing and there's a little grey kitten too who never grows up) she sets out on a journey to break the curse for herself and her friends. Along the way she meets an injured unicorn and a horny-but-moral soldier rendered impotent by a curse after refusing the disguised witch's sexual advances.  After adventures there's a 'happy ever after' for all of the heroes and the witch meets a sticky end.    In the UK the book had a deep red cover with an illustration. I read it in either the 1990's or the early 2000's. Cracking book, definitely for adults given some of the situations, language and humour. Let's say you tell me to produce randomly a number from 1-100, and I choose the number 47. Can it be said that there is a specific reason I chose the number 47, and that it is not completely random? By random I mean that there is absolutely no reason this number in particular was chosen.    It seems odd to me, since it seems like since I have applied conscious effort to produce or choose a number within that range, or even without range, that it can't be truly random, but there might be a reason why I chose that number amongst the many others I could have chosen.  I guess the general question, which I'm interested to know if any philosophers in the past have discussed, is whether our thoughts are necessarily based on prior thoughts, or if thoughts can be truly spontaneous and random? In sysctl, the /proc/sys/net/ipv[46]/conf/ keys have the following subkeys: all, default, and a key for each network interface. For example, on a machine with a single network interface eth0, it will look like this:  iserv ~ # ll /proc/sys/net/ipv[46]/conf/ /proc/sys/net/ipv4/conf/: insgesamt 0 dr-xr-xr-x 0 root root 0 12. Sep 23:30 all/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 default/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 eth0/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 lo/  /proc/sys/net/ipv6/conf/: insgesamt 0 dr-xr-xr-x 0 root root 0 12. Sep 23:30 all/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 default/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 eth0/ dr-xr-xr-x 0 root root 0 12. Sep 23:30 lo/   All the respective settings exist in each key separately. For example, if I want to disable IPv6 Router Advertisements with the accept_ra value, this value exists four times:  iserv ~ # sysctl -a 2&gt;/dev/null | grep "accept_ra " net.ipv6.conf.all.accept_ra = 1 net.ipv6.conf.default.accept_ra = 1 net.ipv6.conf.lo.accept_ra = 1 net.ipv6.conf.eth0.accept_ra = 1   My question now is: which of these values do I need to change? I figured all (to change all existing interfaces) and default (to change all new interfaces that may appear later), but changing these still leaves the value at 1 for lo and eth0:  iserv ~ # sysctl -w net.ipv6.conf.all.accept_ra=0 net.ipv6.conf.all.accept_ra = 0 iserv ~ # sysctl -w net.ipv6.conf.default.accept_ra=0 net.ipv6.conf.default.accept_ra = 0 iserv ~ # sysctl -a 2&gt;/dev/null | grep "accept_ra "   net.ipv6.conf.all.accept_ra = 0 net.ipv6.conf.default.accept_ra = 0 net.ipv6.conf.lo.accept_ra = 1 net.ipv6.conf.eth0.accept_ra = 1   Will the machine now accept Router Advertisements on eth0, or will it not? Is it possible to bake dupliverts into one mesh for the BGE? (I have a large ground landscape that I use as the parent to duplicate trees, and the BGE doesn't support most modifiers.) Is Ubuntu based on Debian unstable or Debian testing? which of the two it is? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want.