So far I've proved the following:   $2n \geq \ln(2n) &gt; \ln(n+2)$   for $n \geq 3 $  The proof must be without the use of calculus but I have no idea on how to proceed.
So far I've proved the following:   $2n \geq \ln(2n) &gt; \ln(n+2)$   for $n \geq 3 $  The proof must be without the use of calculus but I have no idea on how to proceed.
Why is jumping into water from high altitude fatal? If I jump from an airplane straight positioned upright into the ocean, why is it the same as jumping straight on the ground?  Water is a liquid as opposed to the ground, so I would expect that by plunging straight in the water, I would enter it aerodynamically and then be slowed in the water. How do we pass the field api name in lwc for a lightning data table? Why do we have an elementary charge $e$ in physics but no elementary mass? Is an elementary mass ruled out by experiment or is an elementary mass forbidden by some theoretical reason? How do I use the chrome driver in Ubuntu 16.04? It's become clear that last night's (Tues Jan 8th 2019) patches to Windows 7 broke SMB2 networking in Lanman Server.  One or both of KB 4480970 and KB 4480960 results in any OS that uses SMB2 (such as Windows XP, some Windows 7, and same generation server OS' and Mac OS X machines (certainly 10.10, 10.11 not sure about others yet)) being unable to connect to Windows 7 Pro shares.  Client machines repeatedly prompt for login despite credentials being correct. Mapping JSF .xhtml files to no extension Would you recommend using a  or a  field, and why (using MySQL)?   I'm working with PHP on the server side. Should I use center or centering for figures and tables? What is the correct way to center figures and tables (figure, table)?  \begin{center} ... \end{center}   or   \begin{centering} ... \end{centering} Missing return statement in a non-void method compiles I have removed Windows 7 using GParted, and want my computer to boot straight into Ubuntu, but I still get the dual boot screen, how can I fix this? I'm trying to generate a secret key to be used for HMAC SHA-256 signature processing. I've seen many sample of keys with variable length from 32 characters to 96 characters.  What is the ironclad rule for this key size? Proving divisibility of expression using induction Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups Hidden features of Python Can you help me resolve this paradox for a geodesic orbit? Does it maximize proper time to sit still rather than orbit for 1 year? Read Committed Snapshot Isolation vs Read Committed - pros and cons? Footnotes in tables? I would like to have footnotes in tables, but the \footnote command does not work inside a table environment.  Googling one finds that this is , at least in the UK.  That link contains a list of solutions to the problem, but since the author of the FAQ does not believe that this is good style, no comparison is made between the different methods.  I am sure that there are good typographical reasons why in most situations it is undesirable to have footnotes in tables (although I have never come across them), however I have recently felt the need to do just this in a paper I am currently writing.  Therefore I'd like to ask two questions:   What are the arguments against footnotes in tables? If one really must go against the advice in 1., which method (whether considered in the  or not) would you recommend?   Thanks in advance.  Added  In response to ShreevatsaR's comment: I do not much care for where the text of the footnote appears.  I do however insist on the footnote marks being attached to the relevant entries in the table, so that I can avoid having to reference "the second entry in the eighth line of the table", etc... If you multiclass a Warlock and a Sorcerer, then you have a character with both the Spellcasting and Pact Magic features.  PHB Page 101, Sorcerer, Spellcasting, Spell Slots:     You regain all expended spell slots when you finish a long rest.   PHB Page 107, Warlock, Pact Magic, Spell Slots:     You regain all expended spell slots when you finish a short or long rest.   PHB Page 165, Customization Options, Multiclassing, Class Features:     Pact Magic. If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.   Do the spell slots keep their previous method of recovery (sorcerer slots long rest, warlock slots any rest), or do they all act consistently as I am led to believe from the language of the multiclass section? Do they all recover only from long rests as per the sorcerer feature, or can they all be recovered with a short rest because the warlock feature says so? leaflet geojson coordinate problem I just started to play with leflet/geojson a little. But my coordinates are not rendered properly and I have no clue what is going on.  My coordinates are: 52.23943, 4.97599. They work correct with the setView function.  var map = L.map('leaflet_map').setView([52.23943, 4.97599], 15);   But using a geojasonFeature they are, hmmm, 'projected', somewhere east of Somalia.  var geojsonFeature = {             "type": "Feature",             "properties": {             "name": "Coors Field",             "amenity": "Baseball Stadium",             "popupContent": "This is where the Rockies play!"             },             "geometry": {                 "type": "Point",                 "coordinates": [52.23943, 4.97599]             }         };         var myLayer = L.geoJson().addTo(map);         myLayer.addData(geojsonFeature).bindPopup("I am a gjson point.");   Anyone who knows what is happening here?  EDIT  Out of pure curiosity I changed the coordinates around [4.976143930893815,52.23925499011473] and the point appears at its correct location. A known bug!? The book says:     Concentration. Some spells require you to maintain concentration in order to keep   their magic active. If you lose concentration, such a spell ends.   So what happens if, for example, you are already concentrating on a spell, and cast Witch Bolt without concentrating. Would you get the initial arc of blue energy, or would it not even go off?  I am asking if you can cast a spell that says concentration without concentrating for an immediate effect. This would be useful to avoid interrupting your existing concentration. In essence, if you are concentrating on thing A (doesn't have to be a spell since other things need concentration), can you cast a concentration spell getting an immediate effect without losing concentration on thing A?  Since the definition of concentration is to keep the spell active (meaning it is already active) I would think that you would get the initial effect (if it had one) without the need to concentrate on it.