What is the value of $\lim_{n\rightarrow \infty}e^{-n}\sum_{k=n}^\infty n^k/k!$ ?  I have tried initially but could not proceed any further. What I have tried is:  $$\lim_{n\rightarrow \infty}e^{-n}\sum_{k=n}^\infty{n^k \over k!}\\ =\lim_{n\rightarrow \infty}e^{-n}\left[e^n-\sum_{k=0}^{n-1}{n^k \over k!}\right]$$  I got no clue after this. I am not sure if how that limit can be be determined.  Any kind of help will be welcome.
I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it.
I ride regularly in the city with my a few valuables with me. My purse, phone, keys, company ID card etc. I hate having a bag on me while ride so I am looking for a solution to have these few items in a bike bag, but also have them safe if I stop somewhere to run into  a shop or a cafe for 15 minutes.   My original idea was to look for a small saddle or top tube bag that is lockable and also safely locked to the frame, and I can simply leave it there. As it turns out there is no such thing! Or I just did not find it?  My second idea was to search for a similar bag, but which is easily detachable and I can take it with myself as a waist bag for example. Same story, I couldn't find anything like this on the market.  Do you know any bag that could work for me? Or do you have an alternate suggestion for my conundrum?   Thank you very much if you take the time to answer! Ride safe! János The web is littered with any number of pages () giving an existence and uniqueness proof that a pair of squares can be found summing to primes congruent to 1 mod 4 (and also that there are no such pairs for primes congruent to 3 mod 4).  However, none of the stuff I've read on the topic offers any help with actually efficiently finding (ie other than a straight search up to sqrt(p)) the concrete values of such squares.  What's the best way to actually find them ? Is it bad practice to return from within a try catch finally block? So I came across some code this morning that looked like this:  try {     x = SomeThingDangerous();     return x; } catch (Exception ex) {     throw new DangerousException(ex); } finally {     CleanUpDangerousStuff(); }   Now this code compiles fine and works as it should, but it just doesn't feel right to return from within a try block, especially if there's an associated finally.  My main issue is what happens if the finally throws an exception of it's own? You've got a returned variable but also an exception to deal with... so I'm interested to know what others think about returning from within a try block? Where, precisely, does feedback on Community ♦ generated flags go to die? For the most part, I treat "Community" like any other user when handling system raised flags. If they are useful, I mark them as such. If they are noise, I dismiss them as such. The Community user has a static flag weight, so our reaction to them is more or less feedback for developers.  Is this feedback from moderators network wide used in any way to help improve the accuracy of system raised flags? Or, would clicking either button suffice?  I'm asking because our reasoning behind declining a flag is now more precise. Does dismissing some as noise help improve the criteria that ultimately generates the flag?  Edit  Yes, thank you Skype, I realize that  asked a similar question . $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors Can I use Mage Hand to fly by Polymorphing myself and picking myself up with the hand? Could I first cast Mage Hand, then Polymorph into a Tiny creature less than 10 pounds then use the Mage Hand to pick myself up and fly at 30 Ft per turn?  Polymorph says:     The new form can be any beast ... The target's game statistics,   including mental ability scores, are replaced by the statistics of the   chosen beast. It retains its alignment and personality ... The   creature is limited in the actions it can perform by the nature of its   new form and it can't speak, cast spells, or take any other action   that requires hands or speech.   This keeps me from casting spells, which keeps me from just casting Mage Hand to fly as long as I want to over and over. But for that initial duration of the Mage Hand cantrip, could I use the Mage Hand to fly as a Tiny polymorphed creature until the spell runs out? iPhone 4 water damage - how to recover data? How to check the maximum number of allowed connections to an Oracle database? Inequality from Chapter 5 of the book *How to Think Like a Mathematician* This is from the book How to think like a Mathematician,  How can I prove the inequality $$\sqrt[\large 7]{7!} &lt; \sqrt[\large 8]{8!}$$  without complicated calculus? I tried and finally obtained just $$\frac 17 \cdot \ln(7!) &lt; \frac 18 \cdot \ln(8!)$$ How is an instance initializer different from a constructor? My online friend is asking for money in order to visit my home country. Is this a legit request or a scam? On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money? How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$? Consider this limit:  $$ \lim_{x \to 1} \frac{\sqrt x -  1}{ \sqrt[3] x -  1}  $$  The answer is given to be 2 in the textbook.  Our math professor skipped this question telling us it is not in our syllabus, but how can it be solved? How to handle users who don't select answers for their questions? I have Blender 2.79 on my Windows 7 system.    I want to install 2.8, but I'm completing some courses which use 2.79.  If I install 2.8, will it automatically replace 2.79?  Will they interfere with one another?  Thanks. PhD in Europe without scholarship from non-European homeland These wonderful icon overlays that give you useful information in the Windows Explorer are not showing up.   It's the most annoying with Dropbox (I already read ). I just tried reinstalling Dropbox - no help. I have this problem also with the  so I don't think that it is a dropbox problem specifically; and something is wrong in my OS. The OS is actually a pretty fresh clean-install...  OS: Win8 Pro 64-bit. Meaning of Conditional sentences with 'should' and 'happen to' Prettiest way to typeset "C++" (cplusplus)? Writing "C++" in plain text results in an ugly setting, as the '+' signs are too big and too spaced:    I've seen around the web several marcos for typesetting the "C++" symbol, ranging from mild kerning to shrinking, raising and lowering the '+' signs.  What is your version of a \cpp{} macro? Run a batch file in a completely hidden way I'm looking for some way to run a batch file (.bat) without anything visible to the user (no window, no taskbar name, .etc..).  I don't want to use some program to do that, I'm looking for something cleaner. I've found  that uses VBScript, but I don't really like using VBS, either. As you can see, objects are falling down when I run the game. Ground is unable to stop those obstacles. Obstacles are rapidly traveling through y axis. I tried by freezing y axis. And, unchecked Use Gravity. I tried by checking Is Kinematic also. But, if I freeze y axis. Than, obstacles completely freeze through y. If there was no ground than the objects don't fall. Same thing happen when I unchecked Use Gravity. I want those obstacles to move if Player hit them. How to stop those obstacles from falling down?   Info :