Solve the recurrence relation $a_n = 5a_{n-1} - 6a_{n-2} + 3$ with initial conditions $a_1 = \frac{3}{2}$ and $a_2 = 3$
Solve the recurrent relation
Triangle Inequality question with fractions Given $a, b \in \mathbb{R}$, prove that   $$\frac{|a + b|}{1 + |a + b|} \le \frac{|a|}{1 + |a|} + \frac{|b|}{1+|b|}$$  When does equality hold?  The only useful thing I could get (using the triangle inequality) is:  $$\begin{align}1 + \left|\left(a + \frac{ab}{2}\right) + \left(b - \frac{ab}{2}\right)\right| &amp;\le 1 + \left|a + \frac{ab}{2}\right| + \left|b - \frac{ab}{2}\right|\\ &amp;\le 1 + |a| + |b| + |ab|\\ &amp;=(1 + |a|)(1 + |b|)\end{align}$$  But it seems to be inapplicable! Any ideas? Transparent text cut out of background I have this MySQL query using  that is the following:  SELECT *  FROM data_tbl WHERE AES_DECRYPT(data_point,'aBcDeF')='data_1';   I've figured out as much that the equivalent in Postgres 11 is  (F.25.4. Raw Encryption Functions) and the query would look something like this:  SELECT *  FROM data_tbl AND decrypt(data_point,'aBcDeF','aes')='data_1';   At least, the documentation for both leads me to believe that these are equivalent.  The data was dumped from MySQL and imported into PostgreSQL.   The data-point field in MySQL is type varbinary(255) and the values all show BLOB in MySQL Workbench.  The data_point field in Postgres is type bytea and the values all show [binary data] in pgAdmin.    Whether those data types are equivalent, I admit, I'm not sure.  The MySQL query works and finds a record based on he criteria. The PostgreSQL does not, although the record is in there. So it seems like one of three things:   The data types (varbinary(255) vs bytea) are not equivalent The data does not match (BLOB vs [binary data]) are not equivalent The functions (AES_DECRYPT vs decrypt()) are not equivalent   I did try to decrypt the value in PostgreSQL just to see what it is in a readable format by first trying:  SELECT decrypt(data_point, 'aBcDeF', 'aes')  FROM data_tbl;   But that just returned [binary data] for all the rows.  Then I came across  to use convert_from as in:  SELECT convert_from(decrypt(data_point, 'aBcDeF', 'aes'), 'SQL_ASCII') FROM data_tbl;   However, I just get this error:  ERROR:  invalid byte sequence for encoding "UTF8": 0xcf 0xf5 SQL state: 22021   So at this point I'm stumped as to how to resolve the primary issue. The primary issue being doing the equivalent of AES_DECRYPT but in PostgreSQL 11. The last error message isn't so much an issue, but it is likely related to decrypt() not returning the same results.  Any suggestions? How can I copy files from A to B, only including files that exist in B? I'm on Windows 7 Professional, and this is my scenario :  Folder "Asd" (C:\)              Folder "Asd" (D:\) File 1                          File 1  File 2                          File 3  File 3                          File 4 File 4 File 5   I'd like to select the folder on C:\ (without selecting each single file, of course) and copy it over the same folder on D:. Usually, it will copy all files. But what I'm looking for is to copy only files (from C:) that are contained on folder d:.  So in my case I'd like to replace only File 1, File 3 and File 4.  File 2 and File 5 must be ignored.  Is it possible? How do rays of light getting focused at a point create an image?  How are the information of object's shape and dimensions expressed as an image when light rays converge?  Is it understandable by solving wave equation for light? I only ask questions. Am I unwanted? Possible Duplicate:          I've been  for maybe a year to get answers to questions I couldn't find on my own.  I always make an attempt first to find the answer on my own.  As of this posting, I've asked 14 questions.  I only once gave an answer, and it was to a non-technical question, and only because I was really bored and had too much coffee to drink.  I wasn't intending to answer any other questions in the future, because on on my best days I'm only a mediocre programmer, and there are some real geniuses here on StackOverflow who can answer other peoples' questions faster and more accurately than I can.  It actually is my nature.  I am an Aquarian.  We are asker-listeners.  Today I discovered Meta Stack Overflow and started browsing around.  I became familiar with the concept of the "Help Vampire".  I seem to qualify.  I continued reading more posts on the topic and got the distinct impression that people who only ask, and never answer, are less than welcome here, rather despised.  So, should I just go away?  Or should I start contributing answers just to have a answer-to-question ratio of 3-to-1 (I read somewhere that's the average) even though I am less than one eighth as knowledgeable as the 10K+ guys and gals?    Or should I continue as I have begun?  I mean, doesn't a 0-questions-asked user like Jon Skeet need a Blankman?  Yin and yang, you know? ffmpeg synchonization of libfdk_aac (or libfacc) and libx264 How to synchronize libfdk_aac and libx264 streams?  ffmpeg -i pipe_libfdk_aac.fifo -i pipe_libx264.fifo -c copy -f flv flv_stream_pipe_or_rtmp.output   I'm always receiving the same asych in all cases: saving file on file system, rtmp-using or raw pipe out. Is it possible to syncronize them?   ffmpeg version N-66924-gaba61b2 Copyright (c) 2000-2014 the FFmpeg developers built on Jan 15 2015 12:50:29 with gcc 4.6 (GCC) 20120106 (prerelease) configuration: --arch=arm --cpu=cortex-a8 --target-os=linux --enable-runtime-cpudetect --prefix=/data/data/info.guardianproject.ffmpeg/app_opt --enable-pic --disable-shared --enable-static --cross-prefix=/home/qwerty/work/android-ndk-r10b86/android-ndk-r10b/toolchains/arm-linux-androideabi-4.6/prebuilt/linux-x86/bin/arm-linux-androideabi- --sysroot=/home/qwerty/work/android-ndk-r10b86/android-ndk-r10b/platforms/android-3/arch-arm --extra-cflags='-I/home/qwerty/x264 -I/home/qwerty/ffmpeg_build/mp3/build/include -I/home/qwerty/faac/output/include -I/home/qwerty/ffmpeg_sources/fdk-aac/build/include -I/usr/local/include/ -mfloat-abi=softfp -mfpu=neon' --extra-ldflags='-L/home/qwerty/x264 -L/home/qwerty/ffmpeg_build/mp3/build/lib -L/home/qwerty/ffmpeg_sources/fdk-aac/build/lib -L/home/qwerty/faac/output/lib -L/usr/local/lib/ -lrtmp -lpolarssl' --enable-version3 --enable-gpl --enable-nonfree --disable-doc --enable-yasm --enable-decoders --enable-encoders --enable-muxers --enable-demuxers --enable-parsers --enable-protocols --enable-filters --enable-avresample --enable-librtmp --enable-libfaac --enable-libfdk_aac --enable-libmp3lame --disable-indevs --enable-indev=lavfi --disable-outdevs --enable-hwaccels --enable-ffmpeg --disable-ffplay --disable-ffprobe --disable-ffserver --disable-network --enable-libx264 --enable-zlib --enable-muxer=md5 libavutil      54. 10.100 / 54. 10.100 libavcodec     56.  8.100 / 56.  8.100 libavformat    56.  9.100 / 56.  9.100 libavdevice    56.  1.100 / 56.  1.100 libavfilter     5.  1.106 /  5.  1.106 libavresample   2.  1.  0 /  2.  1.  0 libswscale      3.  1.101 /  3.  1.101 libswresample   1.  1.100 /  1.  1.100 libpostproc    53.  3.100 / 53.  3.100 I have the following code that shows either a bug or a misunderstanding on my part.  I sent the same list, but modified over an ObjectOutputStream.  Once as [0] and other as [1].  But when I read it, I get [0] twice.  I think this is caused by the fact that I am sending over the same object and ObjectOutputStream must be caching them somehow.  Is this work as it should, or should I file a bug?   import java.io.*; import java.net.*; import java.util.*;  public class OOS {      public static void main(String[] args) throws Exception {         Thread t1 = new Thread(new Runnable() {             public void run() {                 try {                     ServerSocket ss = new ServerSocket(12344);                     Socket s= ss.accept();                      ObjectOutputStream oos = new ObjectOutputStream(s.getOutputStream());                     List same = new ArrayList();                     same.add(0);                     oos.writeObject(same);                     same.clear();                     same.add(1);                     oos.writeObject(same);                  } catch(Exception e) {                     e.printStackTrace();                 }             }         });         t1.start();          Socket s = new Socket("localhost", 12344);         ObjectInputStream ois = new ObjectInputStream(s.getInputStream());          // outputs [0] as expected         System.out.println(ois.readObject());          // outputs [0], but expected [1]         System.out.println(ois.readObject());         System.exit(0);     } } Which pronoun to refer to "person"? It? He or She? They? "When he found his seat on the plane, Sam recognized the person who was sitting in the seat next to his. It? She? was a woman he knew."  Which is more common/natural? Isn't 'it' more correct – grammatically speaking – than 'she', since 'a person' can be a 'he' or a 'she', and obviously you cannot use the singular 'they' here? Are C-style macro names subject to the same naming rules as identifiers?  After a compiler upgrade, it is now emitting this warning for a legacy application:  warning #3649-D: white space is required between the macro name "CHAR_" and its replacement text   #define         CHAR_&amp;        38   This line of code is defining an ASCII value constant for an ampersand.  #define   DOL_SN        36 #define   PERCENT       37 #define   CHAR_&amp;        38 #define   RT_SING       39 #define   LF_PAR        40   I assume that this definition (not actually referenced by any code, as far as I can tell) is buggy and should be changed to something like "CHAR_AMPERSAND"? "Next tag badge" panel score and answers counter discrepancy On the "Next tag badge" panel of  for C# tag, I see:      92/100 score   88/20 answers     But, when I open the "Select your next badge" panel, there's:     97/100 score   90/20 answers       I'm not sure which one is correct. But I believe that both displays should show the same counts.  The discrepancy is not due to a caching, I've noticed it the first time many weeks ago.  For these particular current counts: I have a single C# answer with 3 votes only in the last 5 days, last upvoted 13 hours ago (2015-10-12 19:30:05Z). So it should not cause the 5 votes and 2 answers difference.  I believe that the counters on the "Select your next badge" are correct and the counters on the "Next tag badge" are wrong, as I have:     Asked 1 non-wiki question with a total score of 6. Gave 90 non-wiki answers with a total score of 97.       Today (2015-10-16), the "Next tag badge" got bumped to 97/100. But "Select your next badge" shows 98/100 already. Would you recommend using a  or a  field, and why (using MySQL)?   I'm working with PHP on the server side. I am trying to perform stepwise regression for variable selection in R.  In matlab, the stepwisefit function is able to work in n &lt; p problems. Trying to use step() for such problems i get the error message AIC is -infinity for this model, so 'step' cannot proceed. Is there a way to modify parameters so i can use step function? When does a Möbius transformation map $\Im(z)>0$ to itself? 16.04 LTS upgrade alert- How to handle it? I am running Ubuntu 14.04 LTS. Today when I logged into my computer I got an update alert saying that I could upgrade to Ubuntu 16.04 LTS. The other options were not now or do not upgrade. If I chose to upgrade will it delete my /home directories and the installed software under /opt and /usr/local ? Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start.  All the questions linked below, as well as others which deal with more specialized books, can be found under the tag  (formerly ).  If you have a question to add, please edit it in. However, make sure of a few things first:   The question should be tagged  It should be of the form "What are good books to learn/study [subject] at [level]?" It shouldn't duplicate a topic and level that's already on the list   Related Meta: Can a quasiclassical electron wave packet in elliptic orbit be formed from bound hydrogen-like eigenstates? Position probability densities of eigenstates of hydrogen-like systems have axial symmetry, so that the wavefunction too much resembles the circular orbits in Bohr's model. I'd like to have a demonstration of correspondence principle, where an electron would be localized to look somewhat like a classical particle, and move in an elliptic (non-circular) orbit around a nucleus.  It seems though that if we try to make a wave packet too localized, then it'll disintegrate (get scattered by the nucleus) too fast to see anything resembling an elliptic orbit. OTOH, if we take it too spread out, it'll have to be quite far from the nucleus so as to avoid hitting it, and thus it'll have high total energy, which may appear to be above ionization threshold (at least partially), after which it'd be quite hard to analytically calculate evolution of the wave packet.  Thus my question is: is it possible to form a more or less localized wave packet, which would (on average) move in an obviously-elliptic orbit (major/minor axes ratio of 4:3 or higher), and only require bound states to fully represent it? If yes, then what properties (FWHM, apocenter, angular momentum etc.) should it have for this to be possible? antonym for beneficiary Is there an antonym for beneficiary that is not simply "giver" or "payer"? I'm looking for a word that roughly mean someone who loses financially in the case of an event. Bluetooth audio delay / lag, reason completely unclear to me I have a bit of an odd situation, and wanted to ask for ideas.   Recently started connecting a JBL Charge 2+ to my MBA 11 inch, mid-2013, via Bluetooth. I noticed that there's clear delay between sound event and sound being audible via the JBL.   The problems persists across applications (so for example, playing video via VLC means the sound isn't synced, same for youtube videos in different browsers, same for mp3s that start playing with a small delay, etc.)  The delay is minor, but noticeable, in the range of 0.5s I'd say.  At first I thought it might be a Bluetooth driver issues, but now I found out the following: just connected another JBL device, a Flip 3 to the same MBA, and the sound plays without noticeable delay. I'm not sure if they use the exact same drivers, but now I'm wondering:   Is there a chance that it's a hardware problem? Didn't really consider this a possibility, but now I'm not sure anymore. How to test, and, ideally, fix this issue? How can I isolate the reason for the audio lag with the Charge 2+?   Any help would be appreciated! I had Windows 8 installed on my system, which I screwed up, and now I run Ubuntu 12.04. While installing, Ubuntu used all the 461 GB of HDD space (one partition).   Now I want to make a new partition of maybe 100 GB or so, in order to install Windows 7 alongside Ubuntu (with a dual-boot). But I can't even get a partition done. I can't change the partition in GParted either - the option is disabled.