Recursive CTE Multiple Levels
Making a recursive CTE like query, but for many records
$\sum a_n$ be convergent but not absolutely convergent, $\sum_{n=1}^{\infty} a_n=0$ Let $\sum a_n$ be convergent but not absolutely convergent, $\sum_{n=1}^{\infty} a_n=0$,$s_k$ denotes the partial sum then could anyone tell me which of the following is/are correct?  $1.$ $s_k=0$ for infinitely many $k$  $2$. $s_k&gt;0$ and $&lt;0$ for infnitely many $k$  3.$s_k&gt;0$ for all $k$  4.$s_k&gt;0$ for all but finitely many $k$  if we take $a_n=(-1)^n{1\over n}$ then $\sum a_n$ is convergent but not absolutely convergent,but I don't know $\sum_{n=1}^{\infty} a_n=0$? so I am puzzled could any one tell me how to proceed? Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers. How do I prove this function is bijective? $$ v(s,p)=2^{p-1}(2s-1). $$ The domain is natural numbers and the codomain is also the natural numbers.  And this one: $$ f(s)=2s-1. $$ The domain is the natural numbers, and the codomain is the odd numbers in the natural numbers.  With this one I would do this to show it's injective: $$ \begin{align} v(s)&amp;=v(s_1)\\ \implies 2s-1&amp;=2s_1-1\\ \implies (2s_1)/2&amp;=(2s_2)/2\\ \implies s=s_1 \end{align} $$ So it's injective since if $v(s)=v(s_1)$ then $s=s_1$.  And to show it's surjective $f(s)=y$: $$ \begin{align} y&amp;=2s-1\\ \implies s&amp;=(y+1)/2 \end{align} $$ Then the function must be surjective since every $y$ is the same as the codomain for $f$.  Am I correct? Why wouldn't the `which` command work for `cd`? I can't find the executable for `cd` either! I tried which cd and it didn't give a path but instead returned the exit code 1 (checked with echo $?). The coreutil cd itself is working, so the executable should be there, right? I also ran a find for cd, but there was no executable file shown. How is it implemented then?  Update:  I don't know if I should ask this in another post but since I think it is good here, I'm expanding (?) the post... So the answer was actually quite simple, there's no executable for that — because it's a builtin — But I've found some builtins (bash shell in Fedora) have the executable files! So builtin -> no executable isn't right I suppose? Maybe an answer explaining what builtins actually are (builtin commands?), which actually is the matter here, rather than focusing more on cd... Some good links posted previously indicate that builtins are not programs... so what are they? How do they work? Are they just functions or threads of the shell? Radeon error atombios stuck in loop The screen goes blank and shows logs me out immediately a while after using multiple monitors.   dmesg shows:  [33786.908877] [drm:atom_op_jump [radeon]] *ERROR* atombios stuck in loop for more than 5secs aborting [33786.908901] [drm:atom_execute_table_locked [radeon]] *ERROR* atombios stuck executing 6DD2 (len 254, WS 0, PS 4) @ 0x6DE0 [33786.908910] [drm:atom_execute_table_locked [radeon]] *ERROR* atombios stuck executing 673E (len 78, WS 12, PS 8) @ 0x6777   lspci | grep -E 'VGA|Display' shows:  00:02.0 VGA compatible controller: Intel Corporation HD Graphics 5500 (rev 09) 03:00.0 Display controller: Advanced Micro Devices, Inc. [AMD/ATI] Sun  XT [Radeon HD 8670A/8670M/8690M / R5 M330 / M430] (rev 83)    explains exactly my situation. But I don't have /etc/modprobe.d/radeon.conf file. I have added the png transparent image with the setting and its not showing transparent black background is seen. I have the base color aluminum and i want to add that logo of png on to it. The image is black letter with transparent background why its showing in white letters and black background. May i know where im going wrong any suggestion or help. I have two tables A &amp; B. Table A id | name | num  Table B id | date | roll  id in table B is a foreign key which relates to the id in table A. I want to get the contents of table B where id is given and also along with that data, I need the name whose id is given from table A. NOTE: cannot use multiple queries separated by commas; need to do both the SELECTs in one query. Does Find My Mac stop working after the system has been wiped? When I visit  I see this:     The "Congratulations! You've earned (badge)" section has dropped down completely beneath the tabs under it. The "You've earned a new privilege!" section has a gap at the bottom:     Shog9 says in comments how to reproduce this:     Gotta have earned a badge, not dismissed the notification, and be looking at your own profile. In electromagnetism, why does nature prefer the right-hand rule over the left-hand rule? At school I learnt the  to remember the resulting direction of different phenomena, such as geometrical cross products, mechanical torque, or the direction a screw will move when turning it. This directions are however decided by humans, and we could have easily defined the directions in the opposite way.  However the right hand rule also predicts phenomena which is not arbitrarily set by humans, but is intrinsic to the nature. If you have a coil in which you put some current, and the nature creates a magnetic field in a direction perpendicular to it, the direction depends on the right hand rule.  My question is, why this direction and not the opposite? Nature tends to be symmetric and not have apparent preferences for two equal options, so in a so why is one direction preferred over the other one? Why doesn't a "left hand" rule apply? Where is "Connect to Server" for ssh connections in Unity? Cannot find "connect to server" in 11.04, looks like unity doesn't have it. Is there other very similar way to connect to another Ubuntu computer via SSH? (not in terminal) I have a normal door, and left to its own devices it will simply rest about 20-30 degrees. It won't swing shut on its own, nor stay open on its own. It hangs a bit in the middle. Convenient enough to catch you elbow when you're not looking.  I'd like the door to stay put wherever we leave it.  I've heard idea such as slipping cardboard in to the hinge to rebalance the door, etc. but no guidelines as to the thickness of that cardboard, or which hinge to change to move it in which direction.  I would hope you can appreciate how I'd rather not make this a task of trial and error and continually removing the hinge and putting it back on, etc.  I've also heard something about lightly bending one of the hinge pins, but not sure how I should go about that, or "how much" to bend it.  So, I'm looking for some tips on how to fix this (and other) door. What algorithm(s) are used by MoleculeModify's GenerateConformers? What is the pronunciation of the possessive words that already end in s? Possible Duplicate:           My name is Greg — this is Greg 's post.  If my name ended with an 's', I am aware of the proper apostrophe usage (James&nbsp;→ James'), but how should this be pronounced?  Phonetically, am I Jameses best friend or James best friend? PostgreSQL, SELECT from max id 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? Can I use the "Scan" button with SANE? I have an HP Deskjet with integrated scanner. It has a "Scan" button on its top, but this button does not interact with the xsane program on my Debian machine: To get a page scanned, I have to initiate the scanning process from xsane.  Is there a setting (or a scan program) that allows me to press the scan button and cause the program to scan a page? The following example must be compiled with XeLaTeX to reproduce the issue.  % arara: xelatex \documentclass{article} \usepackage{fontawesome} \begin{document} Text Text \faMobilePhone\ Text Text \end{document}   Normally I am using TeXworks to compile and view the output. With the internal viewer I am getting the desired result. The following image demonstrates it:    However if I open the pdf with Preview (viewer of Mac) the scaling of the icon fails.     If I open the pdf file with Adobe Acrobat Reader the icon is still scaled correctly. If I print the page my printer is also not able to scale the icons correctly.   If I use LuaLaTeX everything seems to work correctly.   Can you reproduce the issue and do you know a solution? In what order are the dated ordered by? Certainly not alphanumeric order.  ls -lt sorts by modification time. But I need creation time. Flag pop-up hidden beneath answer box (and it's still transparent!) The flag window on (a comment to) the last question is hidden beneath the answer box, as shown in the following screenshot:    Linked: , which is currently  - this is not fixed for flags on comments! I live in an apartment which provides Internet service included in the rent. They use a company called Pavlov for the Internet    wireless seems to be working fine but wired connection is at least %30 faster.  Ethernet, Cat5 outlet is built in the wall, and there is only 1 outlet in each room.  I would like to take this 1 outlet coming out the wall and multiply it into 4 wires, for desktop, Playstation, TV and laptop, without losing any Internet bandwidth.   I have absolutely no idea whether this line is coming from a switch or a router but I have been researching Ethernet splitter, routers, switches, hubs and haven't found a solid answer.   Is there a way I can do this?  This picture cleared up few things:     It seems that an Ethernet switch is to Ethernet as a USB hub is to USB, but with packet inspection.  What is a 10/100Mbps Network Switch, actually, and what is the cap?