$$\mathop {\lim }\limits_{n \to \infty } {1 \over {\sqrt n }} \left({1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }}+\cdots+{1 \over {\sqrt n }}\right)$$ ( Without use of integrals ). I was able to squeeze it from the bottom to ${\lim }=1$, but that's not good enough. I'd be glad for help.
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. :)
Is there a catch-all place on the Stack Exchange network where one can post any question that does not obviously belong to the Stack Exchange sites? Is there a catch-all place somewhere on the Stack Exchange sites where one can post a (any) question that does not obviously belong to any of the Stack Exchange sites?  Sometimes I have questions but I don't want to ask them on other sites (no need for names). I prefer to post it on the Stack Exchange network for various reasons.  If there isn't, are there plans for one? I imagine that if such a site exists, questions on that site can also be moved to other more specific sites when they exists, and it's not to be used to post questions which obviously belong to a specific Stack Exchange site. How to import Illustrator swatch libraries into InDesign - Adobe Indesign Mac? I have a very reach swatch library in adobe-illustrator like food colors and.... But in adobe-indesign I don't have many colors. Why? Can I import them to indesign? How to sort a Google Sheets Query by a custom ordering I have a table of choir members with a “name” and a “voice type” column. How can I write a query that orders them by decreasing pitch level of the voice type (i.e. soprano > contralto > tenor > bass)?  Is there in the  something similar to ?  I also tried the , but it does not seem to have an option for custom ordering, either. I don't know if this is a well-known fact, but I have observed that every number, no matter how large, that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there is $1$ digit. A quick example of what I mean:  $9*99 = 891$ $8+9+1 = 18$ $1+8 = 9$  This works even with really long numbers like $4376331$ Why is that? This doesn't work with any other number. Similarly for $11$ and alternating digits sums. In the Ubuntu dock on Ubuntu 18.04, multiple windows of the same application are grouped and orange dots are shown to tell you how many windows of the application are opened. When you click on the icon, a small screen capture of each of the windows is shown.  However, these screen captures are shown in an order that's based on which window was last active on the desktop. This is something that clashes with the way I use the dock. I'm used to mentally mapping the windows to their dock positions. As such, I will often be trying to get to "the top one" and then I end up needing several clicks before I actually get to the terminal (or some other application) that I was looking for.  Is there some way to make sure that the order of these screen captures does not change whenever a window becomes active? Comment hint not disappearing when I start to type comment If I click "add comment", the comment hint (placeholder; "Request clarification or add information.") is not a hint, but editable text. If I delete the text and click outside of the comment then the hint appears as it should and when I click back into the comment box the hint disappears as it should.   I am on Internet Explorer 10.0.7.  Am I just oblivious and this is how it has always been (having to delete the comment hint), or is this a bug? Make a Bash alias that takes a parameter? I want to render an image as a background image via an inline style in twig. I created a field called bg_image and attached it to the standard plain page.  After fiddling around for hours I was able to get the Image URL in node.html.twig  {{ file_url(node.field_bg_image.0.entity.uri.value) }}   but I could not get it to work inside field--field-bg_image.html.twig  Can I get the node from there anyhow, so I can then get the image?  How can I get the image URL to use as inline style? I thought maybe I can pass a variable from field--field-bg_image.html.twig to image.html.twig and then just render  {{ uri }}   instead of  &lt;img{{ attributes.addClass(classes) }} /&gt;   but I could not get it to pass the variable there unless I use includes  {% include 'image.html.twig' with {'image': image, 'isFromField': isFromField} %}   (isFromField is true, when it comes from the field--field-bg_image.html.twig) But that didn't work either. The Image was never rendered that way.  Would be very glad if you can help - my php knowledge is very basic. Thanks After update, get "error: file not found." followed by "grub rescue> _" In books the equation for length contraction is derived by supposing that the velocity of the spacecraft is the same for both observers. So the question is that, is the velocity really the same for both observers? Whereas there must be some trouble in the velocities noted by observers. I mean: If the observer on the spacecraft measures the velocity of the spacecraft to be $v$ then is it possible for the other observer to measure the same velocity from the Earth? Does the shebang determine the shell which runs the script? Can I have multiple background images using CSS? If I'm playing the Hilltop farm in co-op - what farmer's mining level is used for the hilltop spawns? Is it possible to remove a user's password using the net command?  I tried "net user &lt;name&gt; *" and just hitting return twice, but this does not work as expected. Is there any other way to do this? (I'd gladly take non-net commands, as long as they are built-in in XP SP3).  Edit: Seems, I did not make my intention clear. I don't just want to change the password, but remove it completely (so that the user may log in without having to supply a password).  I'm familiar with the "net"-reference and have searched online for several hours, but could not find a hint on how to do this. Would someone give a thorough explanation of 1.14 Minecraft's /data modify? Okay, so I've been searching all over the internet for an explanation of data modify ever since I heard Sethbling passively mention it in one of his videos. The only  thing I could find on it was the wiki and the update log for the 1.14 snapshot. So, I checked these, and they hardly explained it at all. I can get /data modify block 123 20 123... and that's as far as I get.  Minecraft wiki does not at all define clearly what  is (the thing meant to go after coords), nor does it specify what each operation does to what. Operations include (without explanation, and excluding set (which it does explain)): append, insert, merge, and prepend. Then, it has from|value as the next option, which aren't explained either. After this, it just has block/entity and coords/id. So, I know the format (mostly), but I haven't the slightest idea what any of it means. And nothing I've seen on the internet even mentions the command save for Minecraft wiki itself.  Please explain if you know what data modify is. Thanks! Say that we have a secure random number generation that outputs 32 bit random numbers, so it's output is a true random number between 0 and a MAX.  What is the best way to map this random number to a defined range (say I want something random between X and Y) without loosing too much entropy? Why is it dangerous use a coiled extension cord I have a complex embedded Linux software running on a gentoo derivative, on which a certain piece of code gets executed regularly every ~84 minutes. Sweeping through the main code to find places where this code might get executed was unsuccessful, and crontab also seems no possible explanation.   My question: Is it possible, by modifying the code in question, to find out which other process/code/file/service started it in the first place? Are there some information in the /proc directory I can use? Or is it impossible to find out the process that executed the given code? Estimating the intersection of two lines I have two datasets, A and B, of weighted (x,y) pairs. I computed the best fit lines, L_A and L_B, respectively, of these datasets, and then computed the intersection of these two lines, (x*,y*).  Now, A and B are drawn from random distributions (of the form y=mx+b+e, where e is a normally distributed error term). I'd like to compute a confidence interval around x*. How can I do this?  A naive approach I tried involved computing confidence intervals for the slope/intercept estimates of L_A and L_B, generating approximate distributions for those 4 parameters, and repeatedly randomly sampling from these distributions. But a given line's slope and intercept estimates are not independent of each other, and I wasn't sure how to salvage this approach to account for that. I have two desktops (one of which I'm using as a server), my main machine has a weaker i5 cpu, my server has a stronger i7 cpu. On my main machine I am experiencing stutters because the CPU often runs at full load under regular use (strangely, I also use upwards of 10GB of RAM, no joke... The heaviest program I'm running is google chrome).  I was wondering if there was any possible way to share a cpu from one machine over network to another machine as an emulated processor, which could be used by the client machine in a similar sort of fashion as virtual machines use or "borrow" their host's cpu.  This way I could offload work onto the server's cpu when the main cpu is under full load to prevent annoyances like stutter, and possibly combine both of them for more intense tasks (like decryption, compilation, archiving or other multithreaded stuff)  Does this sort of software exist, or has anyone at least tried to make it? If not, is it feasible?  (This sort of program would also ideally be able to offload data onto the server's RAM for faster processing, since the now common gigabit connections get to have nearly the same speeds as a standard HDD this doesn't sound far fetched either)  To reiterate, what I am primarily looking for is the ability to offload work from a system's main cpu when it is under too much load and forwarding it to another computer's cpu over network.