Is there any place where all current Mathematica bugs are listed?
Is there an issue tracker for already reported Mathematica bugs?
Prove that$$\overbrace{\binom n 0 + \binom n 1 + \binom n 2 + \cdots + \binom{n}{\frac{n-1} 2}} + \overbrace{\binom n {\frac{n+1} 2} + \cdots + \binom n {n-1} + \binom n n} = 2^n. $$   Background:  This problem came from the following link:    and I didn't understand why that was true in which no one on the page has proved it to be so. and i was wondering what was the proof on that Is $K[a,b]=K(a,b)$ for algebraic $a, b$? What can cause a question to be "bumped" to the first page in the Active tab of a Stack Exchange site? (Changing the "Last Active" date.)  . Editing capabilities document in GeoServer I've got several layers in GeoServer, one of which I'm trying to use as a WMS in desktop programs (Manifold 8). I've set it up correctly, but whenever I bring it into Manifold, it projects the layer into EPSG:4326, which unfortunately can't work with my map - I need it in EPSG:3857. The layer in question is wrapped inside a more overarching layer definition, which contains all the layers - and coordinate systems that allow them all to be used flexibly. However, I want to put this layer on its own in the capabilities document, and only allow it to use EPSG:3857. How, in GeoServer, would I edit, or override, a capabilities document? I've been using SSH Tunnel manager to easily set up and stop port tunneling over SSH to various servers at my company. That saved me the pain of opening up a new terminal window which will hang out there just for the sake of having a tunnel open.  This worked great (well , sort of) but SSH Tunnel Manager is a PowerPC application. With Lion, it is not supported any more.  What is a good replacement? Font characters displayed as squares in Ubuntu 18.04 Preventing console window from closing on Visual Studio C/C++ Console application Upper bound on the number of charts needed to cover a topological manifold If $M^n$ is a compact topological manifold (not necessarily with additional structure), is there an upper bound on the number of charts needed to cover $M$ ? Does this bound depend on the dimension of $M$ ?  Thanks in advance...  Cheers How should we cope with 12 month old waking in the night? We are trying to get our 12 month olds sleep routine improved now that both of us will be returning to work.  We've been working on getting the settling routine sorted out each night, and haven't quite yet got to him falling asleep on his own, but he does now settle quickly at the end of the routine in our arms.  We will be moving to trying to get him to settle in his cot soon.  Once settled he will tend to do about 3-4 hours in his cot before waking screaming.  When cuddled he will settle down in about 10 minutes and can generally be put back in his cot.  However often he will wake several times.  Last night he went down at 8, woke at 10, woke at 12, woke at 1am.  Each time putting him back in his cot.   At that point we gave up and brought him into our bed where he slept through to 6am.  When waking up he is often on either all fours or standing in the cot whilst screaming.  The main problem is that he's no longer sleeping "solidly" and will often poke and prod his mum in his sleep, and she therefore doesn't get a great nights sleep.  And with us both back to work we both need our sleep as much as possible. I am having trouble with (a) and (b):  I evaluated (a) and I got that sun of the first three terms does not equal $\ln(5/8)$. I got that it is equal to $\ln(3/4) + \ln(2/3) + \ln(15/16)$ which is not equal to $\ln(5/8)$.  I am also having trouble with part (b). I cannot figure out how to calculate the math to cancel out the $(k+1)^2$ and turn it into $2(n  +1)$.  Any help would be amazing. Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$ How would I go about proving that  $$|a|+|b| \leq |a+b|+|a-b|$$  Using the triangle inequality?  I tried squaring both sides, yielding:  $$|a|^2 +|b|^2 +2|a||b| \leq 2|a|^2+2|b|^2+2||a|^2-|b|^2|$$  Is it correct to move the terms to the other side? I tried $$2|a||b| \leq |a|^2+|b|^2+2||a|^2-|b|^2|$$ Then it is obvious that  $$0\leq |a|^2+|b|^2-2|a||b| +2||a|^2-|b|^2|$$ $$0\leq (|a|-|b|)^2 +2||a|^2-|b|^2|$$ $$0\leq ||a|-|b||^2 +2||a|^2-|b|^2|$$  But I have neither used the triangle inequality, nor it looks mathematically rigorous for my real analysis class. Any tips and tricks for solving these problems? integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. Is there any canon information in Harry Potter that proves one way or another whether a wizard always owns only one wand as a matter of routine?  What I am talking about is a wizard buying and owning one wand and also a second wand (for backup, or simultaneous use, or separate purpose, or ceremonial+work wand), akin to people buying more than one pair of boots, guns or hammers.  A proof would be either canon info showing someone owning 2 wands simultaneously; or a statement showing why that does not happen except in rare exceptions (see below).    NOTE: I am discounting special situations such as winning an extra wand in a duel ala Harry (e.g. the second wand's obtainment wasn't intended/planned), or someone winning a Death Stick from prior owner (in which case it was intended as a replacement wand and not an extra one); or taking another's wand for a time being, ala Voldemort and Lucius Malfoy (since it was more of a "temporary replacement because main wand was useless for the purpose due to paired cores" - far from a normal situation).  Also, I meant wands intended for use - e.g. if Malfoy would have a (imagined by me) collection of rare antique wands, that's as irrelevant as someone having flintlocks in a display case. Probability of complete coupon set in $K$ boxes where a box has $N$ distinct coupons? How can I intercept XMLHttpRequests from a Greasemonkey script? Given a template where the HTML cannot be modified because of other requirements, how is it possible to display (rearrange) a div above another div when they are not in that order in the HTML? Both divs contain data that varies in height and width.  &lt;div id="wrapper"&gt;     &lt;div id="firstDiv"&gt;         Content to be below in this situation     &lt;/div&gt;     &lt;div id="secondDiv"&gt;         Content to be above in this situation     &lt;/div&gt; &lt;/div&gt; Other elements   Hopefully it is obvious that the desired result is:  Content to be above in this situation Content to be below in this situation Other elements   When the dimensions are fixed it easy to position them where needed, but I need some ideas for when the content is variable. For the sake of this scenario, please just consider the width to be 100% on both.  I am specifically looking for a CSS-only solution (and it will probably have to be met with other solutions if that doesn't pan out).   There are other elements following this. A good suggestion was mentioned given the limited scenario I demonstrated&mdash;given that it might be the best answer, but I am looking to also make sure elements following this aren't impacted. Performance Advantages to Iterators? What (if any) performance advantages are offered by using iterators. It seems like the 'Right Way' to solve many problems, but does it create faster/more memory-conscious code? I'm thinking specifically in Python, but don't restrict answers to just that. I gave a scammer my telephone number, address, and name. How bad is it? I'm working with  that has X Y coordinates. They are akin to '3672187.92698000, 534175.72095400'.  I would like to convert them to longitude latitude so they are more like '-90.097017, 29.963176'.  I've seen this  however I don't have that software. I was able to download and install  but I am unfortunately perplexed by its complicated interface. Would like to do the conversion with it, if possible. Rendered image doesn't show what Rendered Viewport shows... (pictures below)