Convergence of $\displaystyle \sum_{1}^{\infty} \frac{1}{n^{\ln n}}$ How can we check the convergence of the given series . I tried a lot of series convergent tests ,but none of them seems to be  working, Please provide me a hint , so that i can proceed it further. Thank you.
$$\sum_{k=1}^{\infty} \frac{1}{k^{\ln k}}.$$  I have some problems with this sum, I have tried most of the common methods, such as the ratio/root test, integral test, etc. I do believe it looks like a problem easily solvable by a direct comparison with some p-series, however, I do not know how to formulate the inequality.   I did try using the common fact that $\ln(x) \ll x^p$ for large $x$ but that of course only bounds it from below with a convergent series saying nothing about ours. Also I tried rewriting the 'summand' as $e^{\ln(k^{\ln k})}=e^{\ln k \cdot \ln k}$ but this did not really yield anything.   Any answer or hint would be greatly appreciated.
Login SSH with .ppk file on Ubuntu Terminal I have a production server. To login to the server I must use a .ppk file.  How to login with Ubuntu Terminal and .ppk file?  I tried this :  ssh -i location/file.ppk username@server-ip   but it is showing an error message. Calculating CR of monsters that do not deal calculable damage Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$ I have some trouble with this: Show that if $a, b \ge 0$, $c, d &gt; 0$ and $\frac{a}{c} + \frac{b}{d} &gt; 1$ then   $$\lim_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$$  we were not really shown how to evaluate multivariable limits other than trying different paths, which wouldn't work when the limit exists, or by applying the squeeze theorem which is my initial plan. Unfortunately I cannot find a proper bound for the denominator and so I am quite lost right now. Any help would be appreciated. Minecraft 1.7.4 server issues with loading world When I set up a site in multiple languages, how should I set up my URLs for search engines and usability?  Let's say my site is www.example.com, and I'm translating into French and Spanish. What is best for usability and SEO?  Directory option:  http://www.example.com/sample.html http://www.example.com/fr/sample.html http://www.example.com/es/sample.html   Subdomain option:  http://www.example.com/sample.html http://fr.example.com/sample.html http://es.example.com/sample.html   Filename option:  http://www.example.com/sample.html http://www.example.com/sample.fr.html http://www.example.com/sample.es.html   Accept-Language header:  Or should I simply parse the  header and generate content server-side to suit that header?  Is there another way to do this? If the different language versions don't have different urls, what do I do about the search engines?    UPDATE 2011-12-06  Google has new recommendations for meta tags for explicitly pointing to other language content: .  UPDATE 2012-05-25  Related but not precisely:   UPDATE 2013-06-12  includes discussion of several URL schemes directly relevant to the question. What is the difference between image size and image quality? I have a Casio EX-S12. It has a setting for image size, but also a separate setting for what it calls "image quality". There are three image quality values: "Fine", "Normal", and "Economy".  The Casio manual is not clear on what image "quality" actually means -- specifically how it's different from image size. All they say is that the "Fine" setting "helps to bring out details when shooting a finely detailed image of nature that includes dense tree branches or leaves, or an image of a complex pattern." I'm confused because isn't this what image size is all about (more pixels = more detail)?  In terms of memory usage, the manual also says that for a 5 megapixel picture, a "Fine" image takes up 2.99 MB, a "Normal" image takes up 1.62 MB, and an "Economy" image takes up 1.12 MB, so this "image quality" setting of theirs is certainly having a significant impact on memory usage.  My question is, what exactly is "image quality", if it's not image size? What is the "thing" that is taking up additional memory?  Thank you. Streaming large files in a java servlet MySQL Query GROUP BY day / month / year Is it possible to batch import Wavefront .obj to blender? I'm working on 2.69. If I select multiple .obj files, only one gets imported. Also if I hit A on file selection window to select all files (.obj and .mtl) I get an error, nothing gets imported. I have to import several hundreds of .obj into the blender file, is this possible? List of tables, db schema, dump etc using the Python sqlite3 API Adding the PHP json extension So I have this word problem and I’m a bit confused about it. I have the answer and explanation but I still don’t understand: The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?     A. Less than 5730 years      B. Approximately 5730 years      C. Significantly greater than 5730 years, but less than 11460 years      D. Approximately 11460 years  Correct Answer: A Explanation: Because the half-life of carbon-12 is essentially infinite, a 25 percent decrease in the ratio of carbon-14 to carbon-12 means the same as a 25 percent decrease in the amount of carbon-14. If less than half of the carbon-14 has deteriorated, then less than one half-life has elapsed. Therefore, the sample is less than 5730 years old. Be careful with the wording here—the question states that the ratio is 25% less than the ratio in nature, not 25% of the ratio in nature, which would correspond to choice (D). How is the ratio of the carbon isotopes relevant to half-lives? What is the purpose of saying the half-life of an isotope is infinite? What is meant by “the normal ratio in nature”? Just based on the answer, it seems like the question said “25% of a carbon sample decayed, how old is this sample?” Obviously it’s younger than 5,730 years (the time for its first half life) because if only 25% decayed that means half a half-life has passed. I don’t see how isotopes and ratios would change this problem at all. Edit: Every answer here was very informative and helpful. It was tough to pick a best answer. I picked Cosma’s because it clicked with me. If you’re reading this and want to understand radiocarbon dating, look at every answer because there is some useful information in every answer How do I kill mobs using /kill without them dropping loot? I have a spawn area I am hoping to make a safe haven, so I have a command block on a clock that kills each hostile mob type. This works to keep the place free of any hostile mobs, however every night I see rotten flesh, bones, arrows, and string everywhere.  I would like to add something to my command blocks so that they are killed without dropping loot. How can I accomplish this?  Note that I want mobs to drop loot generally elsewhere in the world, so /gamerule doMobLoot false will not do the trick for me. I'm hoping for a command that only applies to the mobs killed by the command block, and not anything else. In Harry Potter, we know ghosts became ghosts when they are too afraid of death to go on - I thought about it and I'm quite certain they all go to their own version of Harry's King's Cross and become ghosts when they return as Harry did.  So can they return there? Once they've been a ghost long enough that they no longer fear death, can they move on? 2 orderby in wp_query with 2 custom fields I'm triyng to display hotels (taxonomy which i have created) by two 'orderby' with wp_query but i'm not success.  Results looks likes:  Hotel 1 :       2 persons          5 stars Hotel 2 :       2 persons          4 stars Hotel 3 :       2 persons          3 stars Hotel 4 :       3 persons          5 stars Hotel 5 :       5 persons          5 stars Hotel 6:        10 persons         2 stars Hotel 7:        10 persons         1 star   The first 'order by' is on the number of persons(the biggest in first) and the second 'order by' is on the rating in stars (so, if several hotels have the same number of persons, the hotel with the biggest stars rating would be in first).  Below my code. I have tried to add an array inside an array with meta_query but it doesn't work.  $args=             array(                                     'post_type' =&gt; 'hotel',                                     'Services' =&gt; $Services,                                     'Town' =&gt; $Town,                                      'meta_key' =&gt; 'Number_persons',                                     'orderby' =&gt; 'meta_value_num',                                     'order' =&gt; 'ASC',                                        'meta_query' =&gt; array(                                                            array(                                                                'meta_key' =&gt; 'Rating',                                                                'orderby' =&gt; 'meta_value',                                                                'order' =&gt; 'DESC',                                                               )                                                        )                  );   $the_query = new WP_Query( $args );   Thanks a lot :) How do I stop sharing call history between two iPhones? My husband and I both just upgraded to iOS 8.3.  Now I notice that if I have a missed call it shows up on his notice screen and all my calls show up in his recent call history (and vice versa).  Both phones don't ring and they don't need to be near each other or connected by Wi-Fi.  We do share an iTunes account.  How do I stop sharing call history between the two phones? Why does parameter expansion with spaces without quotes work inside double brackets "[[" but not inside single brackets "["? I'm confused with using single or double brackets. Look at this code:  dir="/home/mazimi/VirtualBox VMs"  if [[ -d ${dir} ]]; then     echo "yep" fi   It works perfectly although the string contains a space. But when I change it to single bracket:  dir="/home/mazimi/VirtualBox VMs"  if [ -d ${dir} ]; then     echo "yep" fi   It says:  ./script.sh: line 5: [: /home/mazimi/VirtualBox: binary operator expected   When I change it to:  dir="/home/mazimi/VirtualBox VMs"  if [ -d "${dir}" ]; then     echo "yep" fi   It works fine. Can someone explain what is happening? When should I assign double quotes around variables like "${var}" to prevent problems caused by spaces? Is there a way to detect the collapse in wave function of entangled particles instantaneously? Is there a machine or instrument which will notify us instantly when the wave-function has collapsed if we have access to only one of the entangled particles? Note that the wave function collapse will be triggered by observing the particle which we do not have. Or in other words is there a way to identify (instantaneously) if the entangled pair of a particle has been observed and the wave function has collapsed. Where does Google Chrome automatically save pages? Is $7$ the only prime followed by a cube?