How to find $\sum_{n=0}^{\infty } \left ( \frac{1}{n.(n+1).(n+2)))} \right)$? $$\sum_{n=0}^{\infty } \left ( \frac{1}{n\cdot(n+1)\cdot(n+2)))} \right)$$  I've tried all of the tests but I couldn't solve this.  Does it converges? What is the sum if it converges?
Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$ 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.
Two seasonal periods in ARIMA using R I'm currently using R to predict a time series with these instructions:  X &lt;- ts(datas, frequency=24) X.arima &lt;- Arima(X, order=c(2,1,0), seasonal=c(1,1,1)) pred &lt;- predict(X.arima, n.ahead=24) plot.ts(pred$pred)   As you can see I've data each hour, and I chose the seasonal period of 24 (one day).  I would like to improve my forecasting using an additional seasonal period in order to include the seasonal component of the week (seasonal length of 7*24=168 data)  Is there any method for this? How do you do it?  UPDATE: I've read  (your) blog page, maybe can I use the external regressors to simulate a second seasonal period? How To Auto-Format / Indent XML/HTML in Notepad++ Why would a slug thrower be more effective against a lightsaber/Jedi than a blaster? From  question about gunpowder in the Star Wars universe it is  that the shot from a  slug thrower is not completely deflectable by a lightsaber. This seems to be listed as an advantage (over blasters) against lightsabers and Jedi.     For example, during the days of the Galactic Republic, mercenaries fearing an intervention by Jedi Knights used rapid-fire slugthrowers that were impossible to completely deflect, unlike blaster bolts.   This doesn't make much sense though. A slug, while maybe not as deflectable should be just as ineffective against a lightsaber as a blaster shot is, due to the nature of a . That is, a blade made of plasma should simply vaporize the slug, should the slug manage to penetrate the containment field.     The weapon consisted of a blade of pure plasma emitted from the hilt and suspended in a force containment field. The field contained the immense heat of the plasma, protecting the wielder, and allowed the blade to keep its shape.   While a slug would seem to be more accurate than a blaster bolt (at least when used by a skilled marksman), I can't imagine that the slug would be faster than a bolt. Or if it is faster I wouldn't imagine it would be so fast that a Jedi would be unable to react with enough speed to block it, either with their saber or with the force. So what is the implied advantage of a slug thrower, versus a blaster, when used against a Jedi? Family of irreducible polynomials The following code works as expected in both Python 2.5 and 3.0:  a, b, c = (1, 2, 3)  print(a, b, c)  def test():     print(a)     print(b)     print(c)    # (A)     #c+=1       # (B) test()   However, when I uncomment line (B), I get an UnboundLocalError: 'c' not assigned at line (A). The values of a and b are printed correctly. This has me completely baffled for two reasons:   Why is there a runtime error thrown at line (A) because of a later statement on line (B)? Why are variables a and b printed as expected, while c raises an error?   The only explanation I can come up with is that a local variable c is created by the assignment c+=1, which takes precedent over the "global" variable c even before the local variable is created. Of course, it doesn't make sense for a variable to "steal" scope before it exists.  Could someone please explain this behavior? Drop rates for set / legendary items Just wondering what the drop rates were for Set / Legendary items, or is it totally random? I imagine they would increase for later acts in Inferno. My monk is comfortable in Act 3 in Inferno, but I've only found one set item, so MF will increase chances for them? Intuitive explanation of the bias-variance tradeoff? I am looking for an intuitive explanation of the bias-variance tradeoff, both in general and specifically in the context of linear regression. How to enlarge Ubuntu system partition to the left? sda6 is ext4 file system and where my ubuntu is installed, 30GB. sda3 is "ntfs" file system and where my windows is installed, 400GB. sda7 is a 50 GB empty partition with "ext4" file system.   How to move the space of sda7 to sda6 to let sda6 become 50+28=78 GB.    Here's a real case of mine :( I want to add more space into my ubuntu (28.2 GB one) from other emtpy partition space. When I am in texture mode one of my objects looks like it is in solid mode. The model is textured like all other models in the scene, but it doesn't look like it is in texture mode.  Screenshot will explain better:      What this model looks like. What all models should look like in texture mode. Error while writing strcat() using pointers What is virtual memory? I was double checking my notes for 'Virtual Memory' and the definition in my text book is:     Process of allocating a section of secondary storage to act as part of the main memory   Where as  says:     Virtual memory is a computer system technique which gives an application program the impression that it has contiguous working memory (an address space)   and (Wikipedia also says)     Note that "virtual memory" is more than just "using disk space to extend physical memory size"   Can anyone offer any clarification as to which is correct? How can I bypass Activation Lock? I bought a used iPhone 4.  The previous owner re-set the phone, but did not remove the device from their iCloud.  It is asking me for their iCloud information when I try to set-up the phone.  I don't have contact with the previous owner anymore.  Is there a way to remove the device from their iCloud so I can use a new one? I am not sure what caused this error, but here is what the whole error says, and also this is sitting as a notification, and preventing me from updating any software using Update Manager - Please provide some assistance or tell me how to figure out what to do to fix it.  Could not calculate the upgrade  An unresolvable problem occurred while calculating the upgrade.  Please report this bug against the 'update-manager' package and include the following error message: 'E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.' Convergent or divergent $\sum_{n=1}^{\infty} \frac{e^nn!}{n^n}$? Combining multiple git repositories Plurals of acronyms, letters, numbers — use an apostrophe or not? When I was in high school back in the 1970s, I was taught that to make a plural of an acronym, a letter, or a number, one should add an apostrophe and "s". Like I would have written this sentence, "... back in the 1970's ..." I would write "one CD, two CD's". Etc. I followed this rule faithfully for years until a co-worker told me it was wrong. Now I can't find any source that agrees with what I was taught.  Is this a rule that has changed over time? Was the convention in the 70s that one should use an apostrophe but this has changed and now we do not? Or were my high school English teachers just confused? I was surprised to discover my dictionary had this entry for dilemma:     a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones   The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a  is specifically based on the number two.  Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic? Support showing image in original size in overlay Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction I am just starting out learning mathematical induction and I got this homework question to prove with induction but I am not managing. $$\sum_{k=1}^n\frac1{\sqrt k}&lt;2\sqrt n$$ Please help! Is it mandatory to have a link to the theme designer? I just wanted to know if it's ok to modify/remove links pointing to the designer of the theme.  In my case I have "theme by" and the site's logotype, would it be ok to remove the logotype and write the site's name? Or remove it altoghether?  Does it have to do with the particular designer of the theme?  Thanks