I tried to solve but could not develop the left part of the equation
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
TRON: Game A.I algorithm? Age replacement policy for hard disks and SSDs at servers I'm planing an age replacement policy for our storage and servers. Most of them are for DBs and some for images (static content) so yes, they have an huge I/O everytime.  Also, we use Samsung 840 Pro SSDs for the RAID Controllers (PERC H700i) as CacheCade.  Are you guys managing the replacement of old hard drives and solid state drives? Context to distinguish "we" inclusive versus exclusive What kind of "mathematical object" are limits? What are the options for traveling to the airports in Paris? Paris has 3 airports (Orly, Roissy, Beauvais), what are the options to go to or to come from there?  (There is also Vatry (XCR) but there is very few flights and i see the shuttle system is currently off.) Applying an ellipsis to multiline text What is the name of the depiction of concentration with raised eyebrow called? Repost it with a minimal working example for the amsmath must be loaded earlier than mathspec problem Is there any way to hide your Steam status from others? Is there any way to prevent others from seeing your Steam status without removing them as a friend?   Let's say I want to play Borderlands 2 without letting some friends know. Is there any way to hide my status to prevent them from knowing I'm playing it?  Basically, what I'm asking if Steam has an "Appear Offline" option. A simple algebra that is not semisimple Search a specific word and copy line to another Sheet I installed blender for the first time, so I have the latest version, 2.78c.  I played with it for a bit.  Then I discovered I couldn't save my work.  I uninstalled it and reinstalled it.  Rebooted.  Same problem.  After a little testing, I realized I CAN save to my NAS storage drive.  I cannot save on my C: drive.  Any project.  Any folder.  C: always fails.  If I run blender as Administrator, it will save to the C: drive.  But not as my normal userid.  So it sounds like a bug of some kind.  I am running Windows 10.  Bitdefender A/V.  I use OneDrive.  I have a 2TB drive installed.  All clean and purring nicely.  Is there a better way to install it?  Or some change I can make (other than always running as administrator)?    Sounds like a bug - but hopefully there's a proper solution.  Thanks,  Jerry Sketch complex curve $z(t) = e^{-1t+it}$, $0 \le t \le b$ for some $b>0$ For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge? For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?  Solution says $0&lt;s&lt;2$.  Any ideas? Almost half of disk space unaccounted for on Windows 7 computer I'm trying to determine what's eating almost half of disk on my Windows 7 Lenovo laptop but haven't been able to determine what.  I read some of the answers on this site but none of the causes seems to be the cause of my problem.  What I've done so far:   Checked Windows' System Restore points but only minimum use, either way I deleted around 2GB if usage from there Used WinDirStat and it came back with a total of 71.3GB usage at the root level C Drives properties says 135GB being used out of 138 GB total, ie, 135 GB - 71.3GB = 63.7GB missing somewhere No "Unknown" files reported by WinDirStat Windows Disk Management utility doesn't report any unused partitions or unclaimed space chkdsk comes out clean Windows disk cleanup tool doesn't report anything big, just small stuff in the lower MB range Lenovo backup tool hasn't been used nor there is a folder for the backup images   Any idea on what to look at and/or do?  EDIT: some additional info... ESTA approved on the same day as B-1/B-2 visa refused I am writing because I have a question regarding my ESTA application and because I could not find a similar case online that would help me at this stage. I have never been to the U.S. so this would be my first visit.    I am a German citizen, hence eligible for the Waiver Program. I applied for an ESTA in June 2014 and got approved. After further research on the Internet I learned that the passport should be valid until 6 months after the planned return date. My passport was due to run out in Feb 2015 - which still should have been fine but because I didn't want to take chances I applied for a new passport which was issued August 2014 and is now valid until August 2024. My passport number has been changed also.    After I received my new passport I was advised by a friend to apply for a B-1/B-2 visa as it would allow me to extend my stay and it seemed like a good idea at first. On the day of my interview I also applied for a new ESTA with my new passport number (just in case) which again was granted.   Unfortunately for me the interview for the B-1/B-2 visa was unsuccessful and I got rejected. I was not aware then that after a rejected interview one could not travel with ESTA, otherwise I would have never risked it!  Now I am very concerned, can I still use my ESTA and enter the U.S.? as I read everywhere that once you get rejected the chances of getting through are very slim and any visa rejection will result in not being able to use the waiver program.  It might be important to note that both the B-1/B-2 interview and the waiver application were on the same day, 21st of August 2014, so depending on how one might look at it that might present a problem too I suppose.  I guess the frustration lies in the fact that I did not need to apply for a B-1/B-2 visa to begin with, and had I not I would now not have these problems. I would like to know how likely it is that I can still travel under the waiver program, if at all, and what my options are at this point. I have got a template class as follows:  class MyClass&lt;T&gt; {     T field;     public void myMethod()     {        field = new T(); // gives compiler error     } }   How do I create a new instance of T in my class? Move the Add Favorite / Ignored Tags boxes to the top It seems that most people who use the ignored tags feature end up with a fairly long list of those tags.  Although , it is sometimes necessary to add new ignored tags manually (typically when adding some-tag*).  It would be a lot easier if the add box was above the long list of ignored tags rather than below. I suppose the same would apply to the favorites tags for consistency's sake. Currently the migration path options from SO are:   Meta.SO Serverfault SuperUser Webmasters Programmers   If we are going to be limited to 5 options, shouldn't we periodically re-evaluate which sites are most appropriate?   (10k only) indicate that the top sites for the last 90 days are:   Superuser - 564 - 5% rejected ServerFault - 278 - 10% rejected Tex - 157 - 13% rejected DBA - 144 - 2% rejected Sharepoint - 127 - 1% rejected Programmers - 126 - 26% rejected CodeReview - 100 - 3% rejected Meta.SO - 81 - 18% rejected Wordpress - 75 - 14% rejected Webmasters - 58 - 8% rejected   All these migrations for sites out of the list required a flag and a moderator to process it.  This is just extra work for the mod team!  If we had the top 5 destinations by volume as the 5 options, we would have had a net savings of 160 flags to be processed.  I suspect we will actually see these numbers change quite a bit if it's easier for users to put questions in the appropriate spot without moderator intervention.  Can we have a review of the migration path list based on migration volume?  Think of the flags! Best choice between using \\ or leaving space after each paragraph to end the paragraph