Lim of $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}$
Help needed with definite integral for $\lim_{n\rightarrow \infty}\sum_{k=1}^{n} \frac{1}{n+k}$
What component to use for audio signal switching? I'm looking to build a guitar pedal switcher based on a Raspberry Pi or Arduino (have not yet decided, but I have an unused Raspberry around and I lean towards that). Anyway, digital logic.  Now, I need to switch audio signal obviously and I need to do it quietly (both physical silence and electrical silence). Please note that the signal is line level throughout most of the build, except for the input which is much lower. I will probably have 2 or 3 loops before the preamp so those may not encounter line level signal.  From what I read and know, so far, mechanical relays are not really an option due to the clicking noise they make. I also read something about FETs, but that's a bit out of my league and I would appreciate any info on these.  PS: I will probably use different power rails for the digital and analog paths.  PS2: The whole thing will be mounted in a 1U rack enclosure, so please tell me if I should take into consideration any thermal issues. Problem using wildcard with apt When I run this command :  apt install libkf5*   I get the following error :  Unable to locate package libkf5*    I'm sure that the packages whose names start with libkf5 exist (tab-completion says so) . So the problem is not about the absence of those packages.(Note the asterisk at the end of that error message , the wildcard's not working at all) I use apt v.1.9. Thanks in advance. Possible to bake texture to new UV map? Initially, my question was: is "focussed" or "focused" the correct past tense of "focus", but since this applies to a lot of words, I would like to generalize and ask: is there supposed to be a rule when to double the consonant? I am running Windows 8.1 N Pro x64 and there are 2 Internet Explorer processes that must be for 32 bit. It stays there even if Internet Explorer is closed. I tried ending the processes but they just come back. I run a x64 Internet Explorer. How can I stop those processes? I do not have much experience in table design. My goal is to create one or more product tables that meet the requirements below:   Support many kinds of products (TV, Phone, PC, ...). Each kind of product has a different set of parameters, like:   Phone will have Color, Size, Weight, OS... PC will have CPU, HDD, RAM...  The set of parameters must be dynamic. You can add or edit any parameter you like.   How can I meet these requirements without a separate table for each kind of product? How do I split a string so I can access item x? Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? Why does `htop` show more process than `ps` In ps xf  26395 pts/78   Ss     0:00  \_ bash 27016 pts/78   Sl+    0:04  |   \_ unicorn_rails master -c config/unicorn.rb                                            27042 pts/78   Sl+    0:00  |       \_ unicorn_rails worker[0] -c config/unicorn.rb                                           In htop, it shows up like:   Why does htop show more process than ps? Question for any programmer—and cat lover—working from his home office. So many times my keyboard is taken over violently by my two cats who think it’s the right place for a nap. And almost every time when they do this I’m was in this precious 100% concentration phases before I get interrupted.  I tried it with a burning an anti-mosquito coil under the desk but they got used to the smell pretty fast.  EDIT: And no I don’t want to keep the cats away completey from my room. Enumerate within TikZ node The + vowel letter I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance. Our iPad is locked and we're not sure of the Apple ID / iCloud password Proof that there are infinitely many prime numbers starting with a given digit string To prove the following fact: given any sequence of digits in any base, eg 314159265358979323 base 10, there are infinitely many primes that start with these digits,eg when expressed in decimal they start with 314159265358979323. I think using a prime number theorem will be helpful . But I am still not getting a point of how to start the proof. What packages do you use and recommend for creating graphics in your LaTeX documents?     As this is a community wiki post, please add your package to the accepted answer (or add a comment, and someone with >100 rep will add it to the CW answer), and include a brief description of what differentiates it from others and how it can be used (GUI drawing tool which generates code, type in raw text, or generates image for inclusion in document).   We'll eventually sort these answers under headings. We want to encrypt / encode URL parameters on our pages. I tried to encrypt a parameter using  with AES algorithm as explained in the   %%[SET @encData=EncryptSymmetric("test", "AES", @null, "1111", @null, "0000000000000000", @null, "00000000000000000000000000000000") ]%% AES: %%=v(@encData)=%%   The result of this function is      AT1r0irnzM+Ax1j8zN+zAw==   Then I tried to decrypt the value using an , but I always received an error message.  I suppose there is a difference between AES algorithm in Marketing Cloud and AES used in the online tool. Indeed if I encrypt the same word with an online tool (128-bit), I received this result      l4Yo3sFofFD1EMmtoh397w==   Do you have any deep information regarding this function? What could be the difference? This  shows the dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$ is $K^{*} = \{(x,t) \mid  \| \boldsymbol{x} \|_{\infty} \le t\}$. Is it right? How is it proved? Testing a UPS by unplugging it from the wall At an Not For Profit/Charity I volunteer for occasionally we were very fortunate to be provided (donated) with a brand new 3Kva APC UPS. This is total overkill for our modest server rack (four mid-range servers and a switch!) but hey, I'll take what I can get!  Pressing the TEST button on the front indicates that yes, the UPS does work. Brilliant. But it only tests it for about 15 seconds.  My question is - will I degrade the UPS by unplugging it from the wall to see how long it will last? My plan is to unplug it, and wait until the battery meter reaches its last LED before plugging it back in, so that I know about how long I will have in the event of a power outage.  Do people do this on a regular basis? I'm guessing no (Lead Acid is very different to Li-Ion batteries)... but what kind of harm would it do if this were to happen (on purpose) every 6 months? Why are lamps and mesh lights not illuminating anything? Is there a clever way to show that  $$|x| - |y| \leq |x-y|$$  I believe I can think of a way to solve this using cases, but the book I'm working out of said that "A very short proof is possible if you write things in the right way" which has motivated me to figure out this quick way, but I've failed thus far and any help would be appreciated Is Unicoins a April Fool’s Stunt? Is Unicoins a April Fool’s Stunt ?