I am to determine if the sequence  $$x_n = \frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n-1}+\frac{1}{2n} $$  converges or not?  I'm thinking I if I can determine if the sequence has some kind om bound and if it is either increasing or decreasing? Because then I know from the Monotone convergence theorem that it converges.  But I'm not sure how you would prove this.
What is the sum of the 'second half' of the harmonic series?  $$\lim_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} =~ ?$$  More precisely, what is the limit of the above sequence of partial sums?
What makes a field not groupable I'm trying to use an aggregate query, but one of the fields I want to group by is not groupable (saw it in the soql error and then verified groupable=false in the metadata).  It's just a number field that holds an integer (number 2,0 in salesforce field spec-speak).  Is there a trick to make it groupable?  Any way around this problem? I don't want to write hundreds of lines of code just to average a list by this field. Internet Accounts spontaneously forgets passwords and I can't reauthorize them I've had this problem before, but I was able to resolve it that time. macOS 10.13.4, everything up to date. Yesterday, Internet Accounts forgot my LinkedIn password and would not reauthenticate. Today, it forgot my Facebook password.   I've tried:   App specific password. Removing the account and re-adding it. Turning off 2-factor authentication. Deleting associated entries from Keychain. Logging out of iCloud, deleting Keychain entries, removing and re-adding the account, then logging back in.   First of all, what the hell—why does this keep happening?! Secondly, what else can I do to fix this short of reinstalling macOS? One who has potential, but never gives the effort to show it.   What would be the best word or words that match this description? Homotopy equivalence of universal cover How to format a USB flash drive? In Windows there is a straightforward "Format" option in a flash drive's right-click pop-up menu. Where's that in Ubuntu? I feel that there is a subtle difference in meaning between 'efficacy' and 'efficiency', but I couldn't find any authoritative sources that could help me confirm or refute this. Is there any difference between the two words, especially in scientific context? Why does light in a room not form constructive and destructive interference patterns? I overseasoned my food, what can I do to remove the strong smell? Large text files load not working on android Does a magic item used as an improvised weapon count as a magic weapon? How long does it take for badges to be awarded? How are they generated? Do badges get calculated in real time, or do they get calculated by an external service? How long does it take for a badge to be awarded, once its requirements are met?  Does Stack Overflow use any external services to do things, like maintenance, e-mailing or badge calculation? While CtrlX works fine in vim under windows, CtrlA selects all (duh).  Is there a way to increment a number with a keystroke under windows? How to roll back Ubuntu to a previous version? I just installed a new version of Ubuntu and I want to roll it back to the previous version.  How can I do that? Is that even possible? ref to subsection number only Why can't an electric field line suddenly break? My book has the following question in it as an exercise:  An electrostatic field line is a continuous curve i.e. a field line cannot have sudden breaks. Why not?  I cannot seem to be able to reason for or against this statement.  Can somebody please tell me why they can't suddenly break and if that were to happen then what will be its outcome? Can more than one antibody bind the same antigen I'd like to clear something up about antibodies that I'm not sure I've understood in the articles I've read. Looking at concepts such as "affinity maturation", "monovalent antigens" and "polyvalent antigens" it seems as if there are multiple antibodies which can bind to the same antigen. (Although I think I'm right in saying that individual antibodies can only bind to one antigen?) However, when I read sentences like "It has been estimated that humans generate about 10 billion different antibodies, each capable of binding a distinct epitope of an antigen" on the Wikipedia page (for antibody) it does make it sound like it's one antibody per antigen? Is this the case? Or is it one antibody per epitope. Either way, to put this question in a nutshell:  Is it true to say that the same substance could bind with (and, therefore, be recognised by) more than one antibody, or not?  Also, if the answer is no, does that mean that antibodies with different binding affinities are classed as the same antibody or not? Every time I insert the SD card from my camera into the card reader, I get this dialog:    Of course there is no need to scan it. Is there a way to disable it? How was Loki not crushed by Mjolnir? Convert a list to a string in C# Why marinade meat with acid or enzymes?