I'm wondering if there is a general solution for $$S_a =\sum_{n=0}^{\infty} \frac{n^a}{n!}$$ with $a \in \mathbb{Z}$ and $a &gt; 0$. From Mathematica: $$S_1 = 1e$$ $$S_2 = 2e$$ $$S_3 = 5e$$ $$S_4 = 15e$$ $$S_5 = 52e$$ $$S_6 = 203e$$
How can I find the value of the sum $\sum_{k=1}^{\infty}\frac{k^n}{k!}$? for example for $n=6$, we have $$\sum_{k=1}^{\infty}\frac{k^6}{k!}=203e.$$
What is the function represented by the power series $$ \sum_{k=2}^\infty\frac{x^k}{k(k-1)}\quad? $$  It looks like $\dfrac1{1-x}$ but I don't know. With the release of iOS 6, the most commonly used mobile browser now supports standard generic image upload buttons. This is actually really handy.  I can take screenshots on my phone or iPad, and use them to answer questions about apps made to run on those devices (or ) to answer questions. Until the release of iOS 6 however, the only way to use these images in my answer was to either sync them over to my computer, and then answer from a desktop, or use a specialized app to upload the images, such as PicUp or DropBox, and then manually write out the markdown code.  After iOS 6, the Image Upload button works just fine, if I switch to viewing the full site from my iDevice, rather than the mobile view. I can upload images directly, and the markdown is handled for me. 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Note: I'm halfway through an implementation for a command-in-question but I just wondered, whether one might be able to use some Unix tools here as well.    Update: Thank for all the answers, I learned a lot today! I would like to accept more one answer, but that's not possible. resetPassword problem for enterprise users when called from a community? I'm working within a custom application in a customer community that is used by both community-license users and Salesforce enterprise users.  There is a custom Visualforce page where an application admin can select a user and reset the password.  The VF Controller is using the standard System.resetPassword() method.  We are finding that when an enterprise user receives this password reset email, the user can't get to the expected password reset page.  Instead, it eventually redirects to the community login screen.  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Showing that Y has a uniform distribution if Y=F(X) where F is the cdf of continuous X Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1}$ is well-deﬁned). Deﬁne a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.  My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$.  But how do you show that it is uniform? Here is a minimal example that showcases my problem:  \documentclass{article}  \usepackage{amsthm} \usepackage{hyperref} \usepackage{cleveref}  \newtheorem{thm}{Theorem} \newtheorem{lem}[thm]{Lemma}  \begin{document}  \begin{lem} Lemma \end{lem}  \end{document}   The warning I get is the following:  [1pdfTeX warning (ext4): destination with the same identifier (name{thm.1}) has been already used, duplicate ignored  \AtBegShi@Output ...ipout \box \AtBeginShipoutBox                                                    \fi \fi  l.16 \end{document}                    {&lt;install dir&gt;/MiKTeX/2.9/pdftex/config/pdftex.map}]   I know that it is just a warning and that, my document will still work perfectly fine with regards to cross-referencing and hyperlinking, but I would still like to know why I am getting this warning and if anything can be done to fix it without removing functionality of the included packages.   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