"E: Unable to correct problems, you have held broken packages" while trying to install 32-bit libraries for Steam
Unable to correct problems, you have held broken packages
Limit of $\prod\limits_{k=2}^n\frac{k^3-1}{k^3+1}$ Calculate $$\lim_{n \to \infty} \frac{2^3-1}{2^3+1}\times \frac{3^3-1}{3^3+1}\times \cdots \times\frac{n^3-1}{n^3+1}$$ No idea how to even start. Partitions of $n$ into distinct odd and even parts proof Let $p_\text{odd}(n)$ denote the number of partitions of $n$ into an odd number of parts, and let $p_\text{even}(n)$ denote the number of partitions of $n$ into an even number of parts.  How do I prove that    $|p_\text{even}(n) - p_\text{odd}(n)|$ is equal to the partitions of $n$ into distinct odd parts. Show that the number of partitions of $n$ for which no part appears exactly once is equal to the number of partitions of n for which every part is divisible by 2 or 3. Show that the number of partitions of $n$ for which no part appears more than twice is equal to the number of partitions of $n$ for which no part is divisible by 3. Can you raise $\pi$ to a real power to make it rational? I am trying to get the Linux distro "PIXEL" to install some PPAS for Wine, and I have run into a issue where it will not install because of the following error:   sudo: add-apt-repository: command not found   I am trying to install wine using the PPA add-apt-repository ppa:ubuntu-wine/ppa and I would like some assistance doing so. If light is an electric and (magnetic field), how can it be absorbed? I was wondering how light or any electromagnetic radiation can be "absorbed" if it consists of electric and magnetic fields. For example if there is a charge at point A, and the  light reaches point A, it will cause that charge to move depending on the value of the electric field. However, why wouldn't this electric field continue on and influence others particles everywhere else? For example, if you have a static charge creating an electric field, then if you put a charge at point A it will feel its effects and then if you bring a charge at another location B it will also feel its effects, namely it will not have been absorbed. Please shed some light on this. Thanks  edit: Does this mean the electron that absorbs this light moves in such a way that it creates an electric field of its own canceling the initial one? Or am I way off? Conventional parenting wisdom tells us to drive the fear of talking to strangers into our kids. Is this at all harmful though? Is there any adverse impact to a child's social development by doing this? How can you balance safety against fear? What are the practical implications of a name change for international travel and activities abroad? I am considering a name change, which seems to be a relatively straightforward action, when one remains in the same country: certain documents are replaced with new ones bearing the new name, and others are presented together with the name change document.  However, I travel internationally multiple times per year, and I often change temporary residence from one country to another. So I often deal with immigration and similar things. Furthermore, I have a lot of things going on like work and studies.  Quite obviously, if I change my name, I would often have to produce a proper translation of the name change document, which may include notarized translation thereof with apostille or, for example, traduction assermentée in France.  However, it would be great to hear about experiences of people, who have dealt with this issue first-hand, so I can weight the disadvantages against advantages of this correctly. In particular, I would like to know if anyone has encountered unforeseen difficulties with this, and how people rate the overall difficulty of such experiences. What is the probability that all three tosses result in the same outcome? A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails is 1/8.  And my question is: What is the probability that all three tosses result in the same outcome?   So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?  If so, we could use the Addition Rule which is $P(A \cup B) = P(A) + P(B)$  where A and B are disjoint events, i.e. $A \cap B = \emptyset$, A is the event of tossing all heads and B is the event of tossing all tails.  I'm not sure how to continue after that... would the complement be used? Don't show pending suggested edits to me after I run out of votes Because the default 'Profile Graph' tool was not sufficient, I wrote a custom VBA script that creates scaled and exaggerated profile cross-sections in ArcGIS but I need more features:   Visualize more than 1 surface Visualize vertical and directional boreholes Ability to symbolize / edit the output Linked with underlying data - changes in terrain (or profile 3D line) reflected in output   A few years ago I tested an extension by A-Prime software called 'CrossView For ArcGIS' but I am not sure if it is compatible with ArcGIS 10 (Contacted A-Prime but they have not yet responded)   Area there any alternatives? Other 3rd party software? A functioning script? that can do this? Catalina not allowing to change read/write permissions despite having SIP disabled Currently Running: macOS Catalina 10.15.1 Issue: Ever since I upgraded to Catalina, macOS is not allowing me to change read and write permissions on system protected files, hence, I am not able to tweak the system as per my likes and dislikes. Steps Tried To Solve The Issue: SIP, always remains . So, no question arises regarding any conflict with system integrity protection. I have also tried to force change the permissions on the system files I want to edit using certain brute force commands, which I can't recall the name of, right now. But, I have tried. As of now, I am still unable to change read and write permissions on system protected files and resources. A more specific question about a tricky redirect case Dupehammer creates and deletes a comment, causing notifications to go out Why is apt-get always using proxy, although no proxy is configured? How can I contribute to Ubuntu? I would like to know what kinds of contributions someone can make to Ubuntu. Such as Programmer, User, Proofreader, etc. Is there anything that is totally random? When I say totally random, I mean absolutely random, not pseudorandom. If I want to say "totally random" numbers such as 1,26,17,4,1 and 27, although I see them to be totally random, they aren't. These are numbers that I think are influenced by my childhood, ideology and everything that I've seen. So, what do you think? Is there anything completely random? How can I disable the volume warning if you raise the volume too much? Where do I ask where to ask? Resource for Blender addons? Can Git hook scripts be managed along with the repository? We'd like to make a few basic hook scripts that we can all share -- for things like pre-formatting commit messages.  Git has hook scripts for that that are normally stored under &lt;project&gt;/.git/hooks/.  However, those scripts are not propagated when people do a clone and they are not version controlled.    Is there a good way to help everyone get the right hook scripts?  Can I just make those hook scripts point to version controlled scripts in my repo?