Obtaining confidence over prediction?
How confident is my model? Is there a way to know?
$$ \sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$$  Does it converge or diverge?   Can we have a rigorous proof that is not probabilistic?   For reference, this question is supposedly a mix of real analysis and calculus. Converting Older United States Dollar Bills Best way to center a  on a page vertically and horizontally? Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? An interesting exercise about converging positive series, involving $\sum_{n\geq 1}a_n^{\frac{n-1}{n}}$ In addition to the .tex and .dvi or .pdf files, TeX/LaTeX/ConTeXt produces and uses lots of other files. What do they do? Which ones are used to create the document and which ones are automatically created by the compiler. What files can I safely delete? How to detect when a variable changes value How can I easily detect when a variable changes value? I would like the execution of the program to break on the debugger whenever a specified variable changes value. Right now I'm using Eclipse's debugger. Can't connect to Android device My Android device won't connect. I've never got MTP to work, I've only ever got it to connect by USB mass storage, which was how it was working most recently. But now, since 13.04, it seems that option has been taken away entirely.  I need to be able to connect by USB to transfer files.  When I plug in the device I get an error that says Unable to open MTP device '[usb:002,003]':    After some web searching, I found that I might need a program called go-mtpfs, so I tried that, and it failed:  $ go-mtpfs /media/MyAndroid 2013/07/16 16:41:43 compiled against libmtp 1.1.5 Device 0 (VID=04e8 and PID=685e) is a Samsung Galaxy Y. 2013/07/16 16:41:43 found device Samsung: Galaxy Y (04e8:685e) @ bus 2, dev 3 :  LIBMTP PANIC: Unable to find interface &amp; endpoints of device 2013/07/16 16:41:43 rdev.open failed: open: open returned nil   How do I get my USB device to just connect, automatically, like it used to? I go to the Minecraft menu and click on singleplayer to test out the 1.9 update. I made a new world (no mods), it said downloading terrain and then it crashes every time (I've tried about 20 times now).  Has anyone else experienced similar issues and know what the fix may be?  Here is the launcher log:  Completely ignored arguments: [--nativeLauncherVersion, 301] [00:35:12] [Client thread/INFO]: Setting user: Teddy_Cromwell [00:35:12] [Client thread/INFO]: (Session ID is &lt;censored&gt;) [00:35:14] [Client thread/INFO]: LWJGL Version: 2.9.4 [00:35:14] [Client thread/WARN]: Removed selected resource pack resources (no region and battle music).zip because it's no longer compatible [00:35:14] [Client thread/INFO]: Reloading ResourceManager: Default [00:35:15] [Sound Library Loader/INFO]: Starting up SoundSystem... [00:35:16] [Thread-5/INFO]: Initializing LWJGL OpenAL [00:35:16] [Thread-5/INFO]: (The LWJGL binding of OpenAL.  For more information, see http://www.lwjgl.org) [00:35:16] [Thread-5/INFO]: OpenAL initialized. [00:35:16] [Sound Library Loader/INFO]: Sound engine started [00:35:18] [Client thread/INFO]: Created: 1024x512 textures-atlas [00:35:26] [Server thread/INFO]: Starting integrated minecraft server version 1.9 [00:35:26] [Server thread/INFO]: Generating keypair [00:35:27] [Server thread/INFO]: Preparing start region for level 0 [00:35:28] [Server thread/INFO]: Preparing spawn area: 5% [00:35:29] [Server thread/INFO]: Preparing spawn area: 8% [00:35:30] [Server thread/INFO]: Preparing spawn area: 15% [00:35:31] [Server thread/INFO]: Preparing spawn area: 21% [00:35:32] [Server thread/INFO]: Preparing spawn area: 27% [00:35:33] [Server thread/INFO]: Preparing spawn area: 34% [00:35:34] [Server thread/INFO]: Preparing spawn area: 42% [00:35:35] [Server thread/INFO]: Preparing spawn area: 48% [00:35:36] [Server thread/INFO]: Preparing spawn area: 56% [00:35:37] [Server thread/INFO]: Preparing spawn area: 66% [00:35:38] [Server thread/INFO]: Preparing spawn area: 74% [00:35:39] [Server thread/INFO]: Preparing spawn area: 81% [00:35:40] [Server thread/INFO]: Preparing spawn area: 91% [00:35:41] [Server thread/INFO]: Preparing spawn area: 98% [00:35:42] [Server thread/INFO]: Teddy_Cromwell[local:E:6d7525a7] logged in with entity id 301 at (244.5, 69.0, 244.5) [00:35:42] [Server thread/INFO]: Teddy_Cromwell joined the game # # A fatal error has been detected by the Java Runtime Environment: # #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x00007fffcf6e6b37, pid=15456, tid=12424 # # JRE version: Java(TM) SE Runtime Environment (8.0_25-b18) (build 1.8.0_25-b18) # Java VM: Java HotSpot(TM) 64-Bit Server VM (25.25-b02 mixed mode windows-amd64 compressed oops) # Problematic frame: # C  [ig8icd64.dll+0x16b37] # # Failed to write core dump. Minidumps are not enabled by default on client versions of Windows # # An error report file with more information is saved as: # C:\Users\Connor\AppData\Roaming\.minecraft\hs_err_pid15456.log # # If you would like to submit a bug report, please visit: #   http://bugreport.sun.com/bugreport/crash.jsp # The crash happened outside the Java Virtual Machine in native code. # See problematic frame for where to report the bug. # AL lib: (EE) alc_cleanup: 1 device not closed Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$ I'm struggling to find the limit at infinity of : $$\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}), n\in\Bbb N$$ I know it is $1$ but I don't understand why this is wrong :  $\sin^2(\pi\sqrt{n^2 + n}) = \sin^2(\pi*n\sqrt{1 + \frac{1}{n}})$.  So $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}) = \lim \limits_{n\rightarrow\infty}\sin^2(\pi*n\sqrt{1 + \frac{1}{n}}) =  \lim \limits_{n\rightarrow\infty} \sin^2(\pi*n) = 0$.  Thanks. What happens to the view.frame.size attribute after a CGAffineTransform (Rotate)? How can I "normalize" the scale of what seems to be either an infinitely large or infinitely small object I'm having issues with an obj file I've imported into Blender. At first I thought the import was broken in some way because the import would go smoothly, but there was no model to be seen. Eventually I figured out that I could snap my view to the object by pressing . on the numpad and it was in fact there, just extremely small or large (I can't tell). I've tried scaling, but the sizes are so extreme that it doesn't seem to be working. Also due to the extreme nature of the object I can only see certain parts of it at a time depending on the angle in which im viewing it at it starts to de-render the parts not directly in front of the camera. Printing a file to a printer in Ruby Why do function pointers all have the same value? I'm trying to use a mask to hide a part of a render layer, so that when the render layer is shown over a movie, some parts in the movie will appear to be in front of the render layer.  For example, assume I want to add a box to this image, so that it would look like it's behind the person:    I created the following simple object:    If I render the object, it looks great - the object is solid, everything else is transparent (I didn't use any 'sky'):     Now I create a mask to describe the standing person (or at least the part that would otherwise be covered by the box):    What I want now is to create a "hole" in the rendered box, so that when I use Alpha-over, the box look as if it's behind the person, but I can't find an easy way to do that. My first guess was to use 'Set alpha' to apply the mask (inverted) as an alpha for the rendered layer, but this doesn't look good:    The mask did create a "hole" where it should, but now all the other pixels are not transparent. How can I "retain" the transparent pixels while setting more pixels to be transparent based on the mask (use it as a matte)?  Note: I can do this with (I'm ashamed to say) some math work on the alpha channel, but it just doesn't seem right:    Thanks, and sorry for the [oh so] long question. What does the dot mean On my reelbox (running Ubuntu) I have found a file in /etc/init that contains the following  # frontpanel-pre - check for frontpanel CAPs and adjust time #  description     "check frontpanel caps"  #start on starting mountall #start on tty-device-added DEVNAME=/dev/ttyS0  task  script         (         /sbin/dev_frontpanel.sh         /sbin/reelfpctl -capability         ) &gt; /dev/.frontpanel.caps         initctl emit --no-wait frontpanel-linked end script   I wonder if the dot in /dev/.frontpanel has some special meaning in linux  I thought the output of the commands in the brackets will be written to a file called ".frontpanel.caps" in /dev/ but there is no such file. In /dev/ there is a frontpanel which is a link to /dev/ttyS0  Could it be, that e.g. echo something &gt; /dev/.frontpanel.caps actually sends data (something in this case) to /dev/frontpanel ?  What does .caps do then? Is `sudo pip install` still a broken practice? Factorial Inequality problem $\left(\frac n2\right)^n > n! > \left(\frac n3\right)^n$ How do I make sure that values from MySQL keep their type in PHP? Why do I get "Required key not available" when install 3rd party kernel modules or after a kernel upgrade? Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta&gt;0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof.