I tried posting this yesterday but I messed up typing the problem and I have now deleted that post (EDIT: oops, turns out you can't delete it after a day, sorry).  I'm trying to solve the problem in the title, but I'm having trouble justifying and making sure my answer is correct.  Also, I know that a problem like this has been solved before on here  but the answers on there make this more confusing since they get $1\over4$ as an answer and they don't seem to justify the answers they get.  So you know what experience I have and how I should try to justify my answer, here is a picture of the chapter and its sections.    I don't know which section the problem in the title comes from. This is also from a calculus 2 course.  Ok, first, if I take the limit of $$\sum_{n=1}^\infty {1\over n(n+1)(n+2)}$$ I will end up with $0$ correct? Since as n gets bigger the denominator also gets bigger meaning the number gets smaller. I'm not even sure if I need to take the limit. Assuming what I just did is correct, that means the series is convergent to $0$, but how would I justify the answer I get? If you look at the chapter I uploaded, is there a test I can use? I have tried reading all of it but it just isn't making sense to me.  Thank you for any help anyone can give me, If I can see how someone would go about solving this, then I should be able to solve the rest on my own.
I got this question in my maths paper     Test the condition for convergence of $$\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)}$$   and find the sum if it exists.   I managed to show that the series converges but I was unable to find the sum. Any help/hint will go a long way. Thank you.
why are the best questions the ones which have been closed? I am trying to classify using randomForest classification in GEE . However, I always get the error User memory limit exceeded, so I assume the number  of the feature are too large. Nevertheless, I saw many developers can classify even bigger dataset, so I am wondering if there is a better option there? The code can be accessed via  var fire= ee.FeatureCollection('users/spatola/recovery_rf_1712').map(function(feature){     var num = ee.Number.parse(feature.get('CLC_311'));     return feature.set('CLC_311', num);   }) var indices= ['EVI_mean','Dnbr','NBR2_mean','NBR2_min','NBR2_max','EVI_min','EVI_max']; var fire1=  fire.filter(ee.Filter.notNull(indices)); var fire2= fire1.select('Class_R','Dnbr','EVI_max','NBR2_max','imageId') var bands= ['NBR2_max', 'EVI_max']; var classProperty= 'Class_R'; var random= fire2.randomColumn('random'); var split_train= 0.8; var split_test= 0.2; var trainPartition= random.filter(ee.Filter.lt('random',split_train)); var testPartition= random.filter(ee.Filter.gte('random',split_test));  var RFtrained_c= ee.Classifier.smileRandomForest({  numberOfTrees: 100,  minLeafPopulation:2,  seed: 123,  }) .setOutputMode('CLASSIFICATION') .train({     features: trainPartition,     inputProperties: bands,     classProperty: classProperty,     }) print(RFtrained_c); var dict =  RFtrained_c.explain(); var test = testPartition.classify(RFtrained_c) print(test.first()) Multiplying two dimensional data by a constant SSH login with clear text password as a parameter? I need to login to a user that I've created on a remote host running Ubuntu. I can't use an ssh key because the ssh login will happen from a bash script ran within a server that I won't have access to (think continuous integration server like Bamboo).   I understand this isn't an ideal practice, but I want to either set the remote host to not ask for the password or be able to login with something like ssh --passsword foobar user@host, kind of like MySQL allows you to do for logins.   I'm not finding this in man ssh and  I'm open to any alternatives to getting around this issue. Does the OS X log notifications from the Notification Center? Why did my windshield freeze instantaneously? It was very cold outside, this morning, when I took the car that slept in the snow, with a simple cloth on the windshield. I entered the vehicle, drove a kilometer or so. The air inside was so cold I could see my breath (or maybe I forgot to brush my teeth). Warm air was blowing on the windshield from the inside and suddenly…  The glass in front of my became opaque, starting from the bottom (the place where the hot air was blowing) and freezing up, up, up until the whole screen was filled in about 5 seconds. It reminded my a little bit of how some baterias spread.  When I tried to remove the mist, I realised it was ice in the car. My windshield instant froze.  I know the theory behind supercooling: a very cold and still liquid can freeze when moved. I'm not sure what happened here, but there were some pretty big turns in the road before it froze. It really looked like the hot air froze the place and not the movement.  Any idea about what happened ? When I tried to connect my Ubuntu 13.10 to my VM Centos 6.5 using ssh appear the message "Connection refused" or "No route to host" even than I change the port, noting change.    I need to use SSH, VPN and Samba, but this IP in my VM Centos do not work.  How Can I resolve this problem? Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$ I'm trying to prove $2^b-1$ does not divide $2^a + 1$ for $a,b&gt;2$. Can someone give a hint in the right direction for this? Lowest voltage drop diode possible I am harvesting energy from an NFC device using a tuned antenna on my PCB. Though this method I am able to generate about 3.05V. I would like to charge a super capacitor using the power harvested from the NFC device. To do this I have  used the simple diode circuit provided  (and shown in Figure 1 below).  The problem I am facing is my circuit requires a minimum of 3V to operate within operating conditions, however with the added drop by typical diodes I believe there with be various situations where the generated voltage will drop below the required 3V. Are there any Diodes available which have ultra low voltage drops of less then 0.01V? and is that even possible?  Please note:   my system load will be &lt; 5mA  The 3.05V generated was without a diode in the circuit Cardinality of set of real continuous functions I believe that the set of all $\mathbb{R\to R}$ continuous functions is $\mathfrak c$, the . However, I read in the book &quot;Metric spaces&quot; by Ó Searcóid that set of all $[0, 1]\to\mathbb{R}$ continuous functions is greater than $\mathfrak c$:  &quot;It is demonstrated in many textbooks that $\mathbb{Q}$ is countable, that $\mathbb{R}$ is uncountable, that every non-degenerate interval is uncountable, that the collection of continuous functions deﬁned on  $[0,1]$ is of a greater cardinality than $\mathbb{R}$, and that there are sets of greater and greater cardinality.&quot;  I understand that (via composition with the continuous function $\tan$ or $\arctan$) these sets of continuous functions have the same cardinality. Therefore, which claim is correct, and how do I prove this? Bounded measurable function and integral with charcteristic function Is there a keyboard shortcut to "unselect" in Windows Explorer? If I've got a file (or files) selected in Windows Explorer, the only way I've found to "unselect" them is click with the mouse on some empty space.  I thought Esc would do this, but it doesn't. Also changing focus with Tab or Shift + Tab doesn't work; the file(s) are still selected even if focus goes to the address bar for instance.  Does anyone know of a keyboard shortcut to do this? Alternatives to 'respectively' If a quadrilateral has a pair of equal opposite sides, and a pair of equal opposite angles, then is it necessarily a parallelogram? I’m sorry I couldn’t upload a photo, so I’ll try to explain it as best as I can.     The quadrilateral has a pair of opposite and equal sides, and has a pair of opposite equal angles (85 degrees in the question).   Can I say this is a parallelogram or not?    I tried drawing a shape with those conditions that is not a parallelogram and I failed. Thanks in advance, and again sorry for not having a photo and I hope I explained it well enough. The question is pretty straight forward. I can get the exit code of the previous command by using $?. But what exactly is it?  I don't think it is a variable, because you can't have any special characters in the name of variable other than _.  foo?foo=10   will result in the error: foo?foo=10: command not found  So if it is not a variable, what is it? Are there others like it? How do I mirror the faces of a cube (edit all of them when I edit one)? Serializing and Deserializing Expression Trees in C# Is there a way to Deserialize Expressions in C#, I would like to store Expressions in a Database and load them at run time. Flex-box: Align last row to grid I applied for a standard visitor visa to the UK for seven days. I earn £278/month and have been working at the same organization for more than a year. I have saved up enough funds for the trip and I attached bank statements to prove it. The ECO refused my visa stating:      I note that you stated that your trip to the UK will cost you £1100, this is approximately 4 times your monthly income. I do not find it credible that you spend this amount on a trip.   I am a single woman, with no financial responsibilities and I saved up for this trip because I really wanted to visit the UK.  How do I prove to the ECO and the authorities that spending £1,100 for my trip wouldn't have caused me any financial harm neither would I have had to access UK government funds?    Another concern of mine is that if I reapply without the partial funding of my father or get sponsored by a different person, does the amount given by my father previously cause hindrance in my visa application?  Won't they still reject it on the basis of my pay being too insignificant? If $A$ and $B$ are square matrices such that $AB = I$, where $I$ is the identity matrix, show that $BA = I$.    I do not understand anything more than the following.   Elementary row operations. Linear dependence. Row reduced forms and their relations with the original matrix.   If the entries of the matrix are not from a mathematical structure which supports commutativity, what can we say about this problem?  P.S.: Please avoid using the transpose and/or inverse of a matrix.