What is the value of the infinite sum of $1+\frac{1}{3}+\frac{1.3}{3.6}+\frac{1.3.5}{3.6.9}+\frac{1.3.5.7}{3.6.9.12}....$ My attempt:  $1+\frac{1}{3}+\frac{1.3}{3.6}+\frac{1.3.5}{3.6.9}+\frac{1.3.5.7}{3.6.9.12}....$  =$1+\frac{1}{6}$.$2\choose 1$+$\frac{1}{6^2}$.$4\choose 2$+$\frac{1}{6^3}$.$8\choose 4$+.......+$\frac{1}{6^{n-1}}$.$2n-2\choose n-1$+...........  But I am perplexed as to what should be my next step?  Options:  (A)$\sqrt{2}$  (B)$\sqrt{3}$  (C)$\sqrt{\dfrac{3}{2}}$  (D)$\sqrt{\dfrac{1}{3}}$  One edit $t_n=\dfrac{1.3.5.7.....(2n-3)}{3^{n-1}(1.2.3....(n-1))}$  $=\dfrac{(2n-2)!}{(6^{n-1}(n-1)!(n-1)!)}$  $=\dfrac{1}{6^{n-1}}$.$2n-2\choose n-1$  Is this going to help me?
Calculating $1+\frac13+\frac{1\cdot3}{3\cdot6}+\frac{1\cdot3\cdot5}{3\cdot6\cdot9}+\frac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $ How to find infinite sum How to find infinite sum $$1+\dfrac13+\dfrac{1\cdot3}{3\cdot6}+\dfrac{1\cdot3\cdot5}{3\cdot6\cdot9}+\dfrac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $$   I can see that 3 cancels out after 1/3, but what next? I can't go further.
What is the best solution for database connection pooling in python? I have developed some custom DAO-like classes to meet some very specialized requirements for my project that is a server-side process that does not run inside any kind of framework.    The solution works great except that every time a new request is made, I open a new connection via MySQLdb.connect.    What is the best "drop in" solution to switch this over to using connection pooling in python?  I am imagining something like the commons DBCP solution for Java.    The process is long running and has many threads that need to make requests, but not all at the same time... specifically they do quite a lot of work before brief bursts of writing out a chunk of their results.  Edited to add: After some more searching I found  which looks decent, but as I'm relatively new to python I guess I just want to make sure I'm not missing a more obvious/more idiomatic/better solution. I read this story a long time ago and cannot remember either the title or the author. It was written in the 60s or 70s. The setting is sometime in the 21 century.  Here is a summary of the plot.  One of the great classical composers (maybe it was Schubert, I'm not sure) is revived with some future technology. All the guys in the lab are very happy about it, the world cheers the achievement. The composer is also quite excited to be alive. Naturally, he is asked to perform a concert. He asks for ink and music paper. Nobody knows what that is: in those days everybody writes music directly in "frequency spectrum" and similar stuff.  The composer, excited to create music again, tries to come up with something but he doesn't like anything he writes. The music is well written, but lacks something essential, it doesn't sound like his real music. Finally, the composer realizes that the lab guys recreated his mind from reviews by music critics, and his music just sounds like that. He performs the concert. The audience enjoys it, applauds and bravos. Not only to composer, but also to the lab guys.   At the end, if I remember it right, the composer gloats over the  primitive taste of the audience. The audience who writes music in frequency spectrum and applauds to lab guys at the music concert did not see the failure in the concert and ate it as it is.  Does someone recognize the story?  PS all the recent talk of advent of AI machines with Machine Learning algorithms reminded me of this story. I'm looking for the name of a sci-fi series, intended for children. Robots have control over the humans. There is a squad of humans who attack them. Every member in this squad has a badge on their suit, and when they touch this badge the suit becomes armed. This series was not cartoon series, it was performed by real people. The main robot character is very similar in style to Darth Vader in Star Wars. The series aired in the 1990s. I am sorry but I can't recall many details. Converting shapefile To GeoJSON using ArcPy? Can spells or spell-like abilities do non-lethal damage? I'm working on a Paladin/Warlock combination, based off of , and as part of this, I noticed Miniman's remark that Repelling Blast won't be that useful, because as a Paladin, you want people up close and personal when you're in a combat situation, not further away.  However, as a Paladin, your creed sometimes leads you to not want to engage in full-blown combat with a potential adversary -- you may want to drive them off or incapacitate/capture them instead.  With this, I wonder: can Repelling Blast, or other spells and spell-likes (such as invocations), be made to do non-lethal damage?  If so, I'm thinking that it'd be useful in exactly that sort of situation -- halting someone/pushing them away without having to wade into a melee with them or blow them to smithereens. The Aleph numbers and infinity in calculus. What is the most efficient way to concatenate strings in SQL Server? I have this code:  DECLARE @MyTable AS TABLE (    [Month] INT,    Salary INT );  INSERT INTO @MyTable VALUES (1,2000), (1,3100);  SELECT [Month], Salary FROM @MyTable;   Output:    I want to concat the Salary (grouping by month) so that it will be NVARCHAR like this: '2000,3100'  How would I do this efficiently? How to determine which Python install is being used by the interpreter? How do you sort du output by size? How do you sort du -sh /dir/* by size? I read one site that said use | sort -n but that's obviously not right. Here's an example that is wrong.  [~]# du -sh /var/* | sort -n 0       /var/mail 1.2M    /var/www 1.8M    /var/tmp 1.9G    /var/named 2.9M    /var/run 4.1G    /var/log 8.0K    /var/account 8.0K    /var/crash 8.0K    /var/cvs 8.0K    /var/games 8.0K    /var/local 8.0K    /var/nis 8.0K    /var/opt 8.0K    /var/preserve 8.0K    /var/racoon 12K     /var/aquota.user 12K     /var/portsentry 16K     /var/ftp 16K     /var/quota.user 20K     /var/yp 24K     /var/db 28K     /var/empty 32K     /var/lock 84K     /var/profiles 224M    /var/netenberg 235M    /var/cpanel 245M    /var/cache 620M    /var/lib 748K    /var/spool I would like to take a picture of a street during the day to depict how much traffic and cars there are on the street.  Is there anyway to do this with a long exposure photograph?  I have a Nikon D90 and I set the f stop down to 1/16 (the lowest of my lens) and set the time to 2 seconds. Doing this, the exposure is almost saturated when taken around 5pm with the sun setting behind a tree. Doing this, the cars passing by were very hard to make out against the stationary background, being visible as a blur in the color of the car.  Perhaps this is not possible and I should just do this at night where the cars lights are much brighter than the background.  Please suggest how else I might depict the traffic in a photograph?  Are daytime long exposure photographs even possible? Where did dedicated.abac.net. come from in my rDNS and PTR records? How can I suspend/hibernate from command line? How can I suspend or hibernate my laptop using command line, without installing additional software? Why is Android refusing to resolve DNS records pointing to internal IP addresses? Is it possible to open a remote terminal session on a Windows XP machine? Remote desktop is... useable, but I'd like to get a proper remote terminal window open on the Windows XP machine, like I'm able to with Linux. A quick Google points at , but it looks like it's only for Vista/Server. Can I remove a digital signature from a DLL? Improper display of parentheses in fraction of fraction The following code:  $\dfrac{\left( \dfrac{\left( \dfrac{1}{2}\right) }{2}\right) }{2}$   gives a nasty output:   It seems that the $\left( \right)$ command doesn't do the job.  Any idea how to solve this in general? Radius of Convergence of power series of Complex Analysis I have come across the following few questions on past exams papers.. I know how to solve these type when it is of the form $a_nz^n$ but don't have a clue what to do with these. Any help would be greatly appreciated!  (i) $\displaystyle\sum_{n=0}^\infty \bigg(\dfrac{1}{2n}\bigg)z^{3n}$.  (ii) $\displaystyle\sum_{n=0}^\infty(2^n+i)(z-i)^n$.  (iii) Show that the radius of convergence of $\displaystyle\sum_{n=0}^\infty z^{n!}$ is $1$ and that there are infinitely many $z \in \mathbb{C}$ with $|z|=1$ for which the series diverges. Determine app sending SMS Premium messages I normally have "Block Premium Messaging" set up on the phones in my family. This is a verizon content block the prevents you (or family members) from sending messages to premium services that charge.  Recently, I had to replace a phone that broke and when the new phone was activated the blocks I had set up were cleared. On my bill was a $9.99 charge for a text to one of these premium services.   I know nobody sent the SMS to the service to sign up for this. I suspect some application on the phone sent the SMS message. Is there a way I can find out which app on my phone is sending SMS messages to premium services? Can I view all the apps that have permission to send SMS messages?  -- update -- well, I ran RL Permissions and no downloaded apps have the Send SMS permissions. I must have already deleted the offending app or something else is going on. For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$ babel shorthand "| doesn't work in macros The package babel with the ngerman option (and most other languages as well, but not english) provides the shorthand "|, which prevents a ligature at the given position (see p. 81 of the , e.g. Auf"|lage will result in the word Auflage without an fl-ligature (as is desired because, in German, you don't want ligatures across morpheme borders).  However, when placed in a macro, "| doesn't work anymore. Why is this and how can I circumvent it?  \documentclass{article}  %\usepackage[T1]{fontenc}% doesn't help \usepackage[ngerman]{babel}  \newcommand{\foo}{"|}  \begin{document}  ff  f"|f  f\foo f  \end{document}