Divergent but bounded partial sums
Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?
"along the river" vs "alongside the river"? In a question on "along" vs "alongside", I have seen this question and the correct answer on the web site makes me confused.      The question is: I enjoyed my walk _________________ the river.  a) along b) alongside  I selected "...along the river" as the correct answer, but on the web site it is shown as wrong and the correct answer is "alongside".  How can that be? I still do not agree, because I have studied the difference between the two. "along" is just the right preposition for thin and long places like road, path, street, beach etc".   So, why would the correct answer be "alongside" which simply means "next to"? Do you not think "along" seems to be better fitting?  Regards,  Note: I would be more than gratefull, if somebody show it to me in a video, like "a walk along the river" and "a walk alongside the river". Maybe I can understand the how "a walk along the river" and "a walk alongside the river" would take place. Old movie about a group of friends with magical weapons fighting monsters I just manually summoned the Eye of Cthulhu, going into battle with copper armour, tungsten broadsword, gold bow, jester arrows and plenty of lesser healing potions. I came rather close to death but I managed to stay alive. However, the Eye took off when I had his health down to ~1700. I'm assuming this means you only have a few minutes to finish it off after a certain point. Is there any equipment I'm missing to help kill the Eye faster and to help my survivability? If it's relevant, my current life is 120. Currently, this site embeds YouTube videos as Flash. (see an example: )  However, this is not the best solution, as now YouTube also supports HTML5, and some users (like me!) prefer to use HTML5 player instead of Flash. Supposedly, it should also work on devices that don't have Flash player (I can't confirm because I don't have one).  The solution seems quite simple: just change the embed code to an iframe, as described at     EDIT:  says:     Note: YouTube &lt;object&gt; embeds were  on January 27, 2015. Please migrate your applications to the , which can intelligently use whichever embedded player – HTML (&lt;video&gt;) or Flash (&lt;object&gt;) – the client supports. If we remove the square in the upper right corner of a $8\times 8$ chessboard.  The question is: Is it possible to cover the entire remaining area, with $1\times 3$ chocolate bars? (they can be laid on the chessboard vertically and horizontally aswell)  For the answer: We know that there will be $63$ squares left on the chessboard, of which $32$ are white and $31$ are black, since the one in the upper right corner was black. $63$ is divisible by $3$, so it could be possible to cover the area, but that doesn't prove that an arrangement exists to do it. I'm not sure how to continue and am seeking help. Thanks. In CSS what is the difference between "." and "#" when declaring a set of styles? What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? Improving your own suggested edit makes you leave the First Posts review queue When reviewing the First Posts (and Late Answers) review queue, after you suggest an edit, you're back in the review queue and the I'm Done button is activated. So far, so good, but when I realize I want to edit something else as well (I often forget the tags), I can click the 'edit' link again. When I'm done improving my suggested edit, I'm suddenly outside the review queue.    This does not happen if you have enough reputation (2k) to edit posts straight away; then you always stay in the review queue. What's the difference between "these" and "those"? First of all, I'm not a native English speaker, but in school I learned that these is used if referring to something near, and those is used when referring to something far away (temporally or locally). But now I'm sometimes watching English movies and notice sentences like "Have you seen those boots?" while the boots were only centimeters away. Is this just not correct, or have I learned the wrong rules?  Another question is, what if I'm referring to something abstract such as ideas or thoughts so that I can't say if they are far away or not. Should I use those or these?  Edit  So it can't be really wrong in any case if I use these respectively those? How come this is happening in java? Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$ As the title says, if a number is divisible by a number, is it always divisible by that number's factors?  An example being that $100$ is divisible by $20$, it is also divisible by $10, 5, 4, 2$ as well?  Does this always apply? GRUB doesn't show Windows 10 Whenever I boot into my system, Linux directly boots. If I press shift, GRUB shows only Linux, not Windows. Here are results of fdisk and update-grub. I think I have installed Linux the wrong way.  $ fdisk WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000     Device Boot      Start         End      Blocks   Id  System /dev/sda1               1  1953525167   976762583+  ee  GPT Partition 1 does not start on physical sector boundary.  $ update-grub Generating grub configuration file ... Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported. Found linux image: /boot/vmlinuz-3.19.0-32-generic Found initrd image: /boot/initrd.img-3.19.0-32-generic Found memtest86+ image: /boot/memtest86+.elf Found memtest86+ image: /boot/memtest86+.bin   No volume groups found done Is there a way to transfer more than one Pokemon at a time? Is there a way to transfer more than one Pokemon at a time to the professor?  Or possibly an addon that gives me this ability?  Vendoring all the trash Pokemon for candies individually is really annoying and time consuming. Why is it called the Millennium Falcon? I'm particularly interested in how the "Millennium" part pertains to the ship itself. It wouldn't hurt to explain the "Falcon" part either though. Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance and covariances. I am wondering if there can be a case for which the joint probability of two Gaussians is not Gaussian? I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects. Proving that two matrices are congruent, in order to establish a rank and signature result. What licence is subscriber content provided under 4.0, 3.0 or them all? In the footer it says:     site design / logo © 2018 Stack Exchange Inc; user contributions licensed under  with . rev 2018.8.7.31273   However, in the footer under Company > Legal > '6. Content Permissions, Restrictions, and Creative Commons Licensing' it instead doesn't specify which CC BY-SA licence we're releasing our content under. It also links to the CC BY-SA 4.0 license:     The CC-BY-SA Creative Commons license terms are explained in further detail by , but you should be aware that all Public Content you contribute is available for public copy and redistribution, and all such Public Content must have appropriate attribution.   Since  if subscriber content is only provided under 4.0, where the footer says 3.0 it can cause users to break the licences.  The footer under Area 51 also mentions that content is licensed under CC BY-SA 2.5.  Since it's not defined which version of the license the content is provided under, I also interpret it to potentially mean all the versions.    What license is subscriber content licensed under? How is unattended-upgrades started and how can I modify its schedule? I'm wondering who starts unattended-upgrades in my debian-jessie:   my man page   DESCRIPTION    This program can download and install security  upgrades  automatically    and  unattended,  taking care to only install packages from the config‐    ured APT source, and checking for dpkg prompts about configuration file    changes. All output is logged to /var/log/unattended-upgrades.log.    This  script  is  the backend for the APT::Periodic::Unattended-Upgrade    option and designed to be run from cron (e.g. via /etc/cron.daily/apt).  But my crontab doesn't show anything by crontab command:  @stefano:/etc/cron.daily$ crontab -l no crontab for stefano # crontab -l no crontab for root  But my unattended-upgrade work fine!(my unattended-upgrades log file) :  2017-02-05 12:42:42,835 INFO Initial blacklisted packages:  2017-02-05 12:42:42,866 INFO Initial whitelisted packages:  2017-02-05 12:42:42,868 INFO Starting unattended upgrades script 2017-02-05 12:42:42,870 INFO Allowed origins are: ['o=Debian,n=jessie', 'o=Debian,n=jessie-updates', 'o=Debian,n=jessie-backports', 'origin=Debian,codename=jessie,label=Debian-Security'] 2017-02-05 12:43:15,848 INFO No packages found that can be upgraded unattended   Where do I have to check/modify if I want to change my schedule? How can I animate an object fading out? Using the Well Ordering Principle to Show that n^3 - n is divisible by 6. I read the following two sources and I think I understand the structure of proofs involving WOP, but I am stuck on the open-ended part where you prove P(n-1) for the  following problem:    Use the well-ordering principle to show that n^3 - n is divisible by 6.    Any help would be greatly appreciated!   Note: After factoring out (n-1)^3 - (n-1) it took the form of n^3 - 3n^2 + 2n and the only difference between that and n^3 - n is "3n^2 - 3n" which I proved was divisible by 6 via induction. Is there a better way to solve this problem?  Edit: , post is useful however I not supposed to use induction for the main part of the proof.