How to show that, $\sum_{n=1}^N 1/n$ $\le$  1 + logN, for N$\ge$5
I want to show that $$\log N&lt;\sum_{n=1}^{N}\frac{1}{n}&lt;1+\log N.$$ But I don't know how to show this.
It is becoming more common for people to explicitly state the pronouns to be used in addressing themselves: he/him, she/her, or they/them. For example, a name tag for a conference might read:  Cory Lopez Some Company She/Her   Usage seems to have settled on the singular they and them as gender neutral pronouns. Alternatives that were once widespread in niche communities, such as sie/hir, seem to have died out.   Whether or not one agrees with this language  shift, the pairing between subject and object case is fixed.  It's difficult to imagine someone who uses "he" as his subject case using anything but "him" as object case, and it's even harder to imagine that such a person would succeed in getting people to use a non-obvious collection of personal pronouns. (And you may see what I did -- flat out assumed that "he" and "his" automatically go together.)  What are the roots of the practice of presenting subject and object case pronouns as opposed to just subject case, subject and possessive, or some other combination?   (Note: I am not interested in a discussion of the gender politics and cultural shifts involved, just the mechanics of how the current representation was chosen.) After installing Ubuntu Studio 12.04, I have found that it uses a low latency kernel.   I searched for an explanation and how to change back it to a real-time or generic one. However, it looks like this part of Linux hasn't been covered to explain the details.   Q: Why choose a low latency kernel over a generic or real-time one?  PS: I have already read the answers from  question and  post. Why didn't the machine affect Bond in Spectre? Can I choose to use only Shapiro-Wilk? How do you find the transfer function of a controller? Below is a block diagram of the system. I thought the circle symbol with the plus and minus sign was an op-amp but I'm not sure whether that's the case. I want to find the closed loop transfer function. If there was no feedback (open loop), then I think I could find the output as Y(s) = Vin*G. This would mean that the transfer function is Y(s)/Vin = G.  Any ideas for how to find the closed loop transfer function and what the circle means? missing $ inserted error for equation I get the missing $ inserted error for the following code:  \begin{equation}  C = $ \frac{2}{\omega^2N^2\mu\pia} $  \end{equation}   I have tried out different changes based on Googling for this error, but nothing seems to help. Any suggestions would be appreciated. Importing a material from blender to unity Evaluate  $$\int\frac{e^xdx}{(e^{2x}-1)(e^x+1)}$$  I tried to decompose the integrand into A and B partial fractions.  No success. How to debug EntityMalformedException? I've got fatal error EntityMalformedException: Missing bundle property on entity of type node. in entity_extract_ids() (line 7700 of .\includes\common.inc) when trying to access user/xyz.  I tried to retrieve info about the malformed node at line 7700, where the error message is built, thinks like :  if (!isset($entity-&gt;{$info['entity keys']['bundle']}) || $entity-&gt;{$info['entity keys']['bundle']} === '') {  dpm($info);// or dpm($entity);  throw new EntityMalformedException(t('Missing bundle property on entity of type @entity_type.', array('@entity_type' =&gt; $entity_type))); }   dpm($entity) returns an unexpected user object, and $info a huge qty of things.   Could somebody put me on the right way ?  I already read whatever I could find about Missing bundle property errors, but none helped solving.  dpm($entity) returns  uid (String, 2 characters ) 70 name (String, 9 characters ) John pass (String, 55 characters ) $S$DUwPuOuDPiDL4nRTYXqc7a5uOfMKey7pyhOFUEKka1XM... mail (String, 30 characters ) john@example.com theme (String, 0 characters ) signature (String, 0 characters ) signature_format (String, 13 characters ) filtered_html created (String, 10 characters ) 1396286331 access (String, 10 characters ) 1397146661 login (String, 10 characters ) 1396513460 status (String, 1 characters ) 1 timezone (NULL) language (String, 2 characters ) fr picture (NULL) init (String, 30 characters ) john@example.com data (Array, 5 elements) roles (Array, 1 element) og_user_node (Array, 0 elements) message_subscribe_email (Array, 1 element) field_bio (Array, 0 elements) field_name_first (Array, 1 element) field_name_last (Array, 1 element) field_facebook_url (Array, 0 elements) field_linkedin_url (Array, 0 elements) field_twitter_url (Array, 0 elements) user_trusted_contacts (Array, 1 element) group_group (Array, 1 element) group_access (Array, 1 element) metatags (Array, 0 elements) rdf_mapping (Array, 3 elements) realname (String, 13 characters ) John Doe content (Array, 13 elements) entity_view_prepared (Boolean) TRUE privatemsg_disabled (Boolean) FALSE What does "no long range" mean on the soulknife rogue subclass mean? How do you reopen a closed question? How can I install Celestia on Ubuntu 18.04.1? Can you cast a spell learned from the Magic Initiate feat using spell slots? Can you cast a spell learned from the Magic Initiate feat using spell slots? Say I play a wizard who learns cure wounds by taking the Magic Initiate feat. Could I cast that spell using the Wizard's spell slots? I've installed Ubuntu 13.04 two times on my PC. Each on a different partition. I would like to delete the one which I'm not using. How would I do that? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. Could "them" mean "those"? Background Nowadays, I see &quot;them&quot; used to mean &quot;those&quot; a lot. I don't know if it was as common in the past. For example, take &quot;one of &quot;. On researching about it, I found some people say it comes from a dialect of British English. Some others say it is a &quot;non-standard&quot; usage. I see this usage in Canadian English also, and it seems some people use it in a sarcastic way. Moreover, I have seen a song titled &quot;one of them days&quot;. I also read, in the book called &quot;A Broken Promise&quot;, &quot;&quot; Finally, Wikipedia says that it is a usage in  (a common name for the Southern Midland dialect of American English):  Pronouns and demonstratives &quot;Them&quot; is sometimes used in place of &quot;those&quot; as a demonstrative in both nominative and oblique constructions. Examples are &quot;Them are the pants I want&quot; and &quot;Give me some of them crackers.&quot;    Question(s): What would you say about the usage of this word? Is it correct? Could we use it in daily speech? Could this usage go beyond a specific dialect and be used in other dialects, regions, etc.? Does it really originate from Appalachian English? Why did this usage become popular among other English speakers? Note: I have already seen a similar question:  However, it only says, &quot;ungrammatical,&quot; there. This question is specific to this situation only, and there is more to it. Seeing as C# can't switch on a Type (which I gather wasn't added as a special case because is relationships mean that more than one distinct case might apply), is there a better way to simulate switching on type other than this?  void Foo(object o) {     if (o is A)     {         ((A)o).Hop();     }     else if (o is B)     {         ((B)o).Skip();     }     else     {         throw new ArgumentException("Unexpected type: " + o.GetType());     } } My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well? How to make Gmail automatically label incoming emails I would like to set it up so that Gmail labels incoming mail based on which business email of mine the emails are sent to. I have two business emails that come to my Gmail account.  For instance, if someone emails me at example@firstbusiness.com, I would like the email to be automatically labeled first business. If someone emails me at my other email address (which also is forwarded to Gmail), example@secondbusiness.com, I would like that email to be automatically labeled second business.   Is there any way to do this? How to assign vertex groups and bone weights through Blender's Python API? I'm making a script to import custom objects, it is still at early stage but so far vertices, faces and uv are created correctly. I want to do weight painting through Blender's Python API but I don't know how to do it properly.  Below an extract of the code that create the objects, how I could add vertex group and relative weights? I know how to extract vertex indices and weights from the input model but don't know how to use them,   (Blender version is 2.72)      for i in range(0,self. subsetCount):         subset = self.subset[i]         coords = subset.getV3(0)         faces = subset.getIndices()         me = bpy.data.meshes.new(subset.name+"_Mesh")          ob = bpy.data.objects.new(str(i).zfill(2)+'_'+subset.name, me)         ob.location = (0, 0, 0)         bpy.context.scene.objects.link(ob)          me.from_pydata(coords, [], faces)         me.update(calc_edges=True)          mat = bpy.data.materials.new(subset.name)         mat.diffuse_color = (random.uniform(0.0, 1.0), \                              random.uniform(0.0, 1.0), \                              random.uniform(0.0, 1.0))         me.materials.append(mat)          for f in me.polygons:             f.material_index = 0             f.use_smooth = 1          # vert_uvs = subset.getV2(0x28)         # if len(vert_uvs) &gt; 0:         #     me.uv_textures.new("UV0")         #     uvlist = [uv for pair in [vert_uvs[l.vertex_index] for l in me.loops] for uv in pair]         #     me.uv_layers[-1].data.foreach_set("uv", uvlist)   edit  found this to add the group:          vxgroup = ob.vertex_groups.new("group")   still don't know how to set weights for vertices (best would be at once)  edit  I was hoping to use something like a foreach_set but can't figure out how to use it, instead solved this way:          for grp in ob.vertex_groups:             grp.add(range(0,len(me.vertices)), 1.0, 'REPLACE')   is just an example and set all vertices weight in all groups of the object ob (if you try it in console select another mesh then back to see the weights applied).