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I have been reading the top posts here, and the recommendations for what to invest in are often similar. What I'd like to know, in as simply of terms as possible, is what the consensus is on priority of these investments.  I am new to this, but here are some of the obvious options:   Paying off credit card debt Paying off mortgage / student loans 401k up to employer match 401k past employer match IRA Emergency fund Other important investments that I have missed   Clearly this will vary person to person, but if you were asked to put an ordered recommendation on a highway billboard, what would it be?  (For example:   Pay off credit debt Emergency fund for 6 months 401k up to match ... ) I am trying to evaluate the following sum. Here $x\in\mathbb{R^{+}}$. $$f(x)=\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$$ At present I do not know how to proceed. Any hints are appreciated. Thanks. How to learn commutative algebra? I want to learn commutative algebra from scratch. I was wondering, as you are experts in mathematics, what you think is the best way to learn commutative algebra? Is there any video course available for commutative algebra? Will there be some online course for commutative algebra on some website like Coursera, etc?  I know noncommutative algebra up to the Artin-Wedderburn Theorem. Also, I know group theory up to the Sylow theorems and Galois Theory. I also know some basic topology.  I'm new to this site so I don't know what tags I should add for this question. Please feel free to edit my question.  Edit 1: I want to learn commutative algebra for learning Algebraic Geometry. Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $ Problem: Show that $\int_{0}^{\infty}|\frac{ \sin x}{x}|=\infty $ .  Here is what i have tried :  I found out that for all $x&gt;0$ , $x-\frac{x^3}{6} &lt; \sin x &lt;x $  . So $1-\frac{x^2}{6}&lt;\frac{ \sin x}{x}&lt;1$ . So applying integration to both side from $0$ to $M$ we have $M-\frac{M^3}{18}&lt;\int_{0}^{M}|\frac{ \sin x}{x}|&lt; M$ . Now we send $M \rightarrow \infty$ and observe that left-hand side goes to infinity . Hence proved .  Please point out if there is anything wrong with my approach . I will also be delighted if could provide alternative solutions . Thank you . Inaccurate altitude GPS data with my Android? How to check if a String contains another String in a case insensitive manner in Java? I am looking for a way to get the 15 character entity ID for a custom field on my Lead object in an Apex controller. I have tried this:  private String getEntityIdFor(String fieldName) {         Map&lt;String, Schema.SObjectField&gt; fieldMap = Schema.SObjectType.Lead.fields.getMap();         return fieldMap.get(fieldName).getDescribe().getId();     }    Of course, there is no getId() method, but this is the closest I got.   Thanks for any help. I think there's an unintended motivation for users to post questions to higher-traffic Stack Exchange sites rather than their more specific or appropriate lower-traffic ones.  I think I have a solution.  What motivated this suggestion for me was that I am confident that if users were to post Android design questions to  beta and/or , that they would likely not be noticed by the appropriate audience compared to the vast army of Android experts here on Stack Overflow.    There are plenty of Android questions on SO that really should be on one or both of the aforementioned sites.  Presently there is little motivation for users to start questions like this on the appropriate site.  Is there something we could do to cross-pollinate related sites?  For instance, what if we let certain tags span certain sites?  Obviously the selection would be controlled by high-reputation users.   There could also be a feature to show (or explicitly hide) certain questions from other sites regardless of the tags.  This could be controlled by lower-reputation users than the global tag since it wouldn't have much statistical impact.  For instance, the android-layout tag could by default span sites, but OPs and other users could eliminate from the Graphic Design site questions that are of a purely technical nature.  Users interested in Android tagged questions would see related questions on design and UE sites--whether they are searching, posting, or viewing a question through the related items.  This would help eliminate cross-site duplicates, and encourage people to post on the correct site in the first place.   For related question lists and search results, there could even be a specific cross-site icon  next to an off-site question to show that it's from UX, for example. Solve this integral for free WiFi AMD-V is not enabled in VirtualBox on AMD APU Why does parseInt yield NaN with Array#map? From the :  [1,4,9].map(Math.sqrt)   will yield:  [1,2,3]   Why then does this:  ['1','2','3'].map(parseInt)   yield this:  [1, NaN, NaN]   I have tested in Firefox 3.0.1 and Chrome 0.3 and just as a disclaimer, I know this is not cross-browser functionality (no IE).  I found out that the following will accomplish the desired effect. However, it still doesn’t explain the errant behavior of parseInt.  ['1','2','3'].map(function(i){return +i;}) // returns [1,2,3] MySQL: Allow both remote AND local connections When working with an image in Photoshop, I'd like to have a simple keyboard shortcut, like in , that automatically does:   Export > Export As or Export > Save For Web  Resize to biggest dimension = 600px (either width or height) Add suffix _600.jpg to filename   How to do that?  I'm not sure how to edit a recorded macro to do that (add the suffix and choose 600px for the biggest dimension).  Example: you open myphoto.png, you press F6 and then you automatically get myphoto_600.jpg. Execute shell script or command on idle time I'm searching for the possibility to execute a shell script or command based on idle time in the bash shell.  As an example, if I'm in a SSH session to a server of mine and after X minutes of inactivity in the terminal, I want a command to start a desired program like cmatrix, and when I come back and press a key I will get back where I left. How to integrate a paper where I am third author, but did a lot of work, into my master's thesis? I am writing my thesis currently and I want to include papers that I am included on as an author.  I will have a couple papers where I am 1st author, but there is one where I am third but did a lot of the work.  How do I go about integrating it into my thesis?  Can I copy/paste most of the text still or do I need to rewrite it?  I don't want to plagiarize but don't want to rewrite it if I don't have to. How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure? I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure I did not get any of them. How can this be possible?  Here is the code:  fit5_snow&lt;- lm(Response ~ Stimulus, data=audio_snow) anova(fit5_snow)  &gt; anova(fit5_snow) Analysis of Variance Table  Response: Response           Df Sum Sq Mean Sq F value  Pr(&gt;F)   Stimulus   5  73.79 14.7578  2.6308 0.02929 * Residuals 84 471.20  5.6095                   --- Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1   df&lt;-df.residual(fit5_snow) MSerror&lt;-deviance(fit5_snow)/df  comparison &lt;-  HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)  &gt; comparison &lt;-  HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)  Study:  HSD Test for audio_snow$Response   Mean Square Error:  5.609524   audio_snow$Stimulus,  means                  audio_snow.Response   std.err replication snow_dry_leaves            4.933333 0.6208034          15 snow_gravel                6.866667 0.5679258          15 snow_metal                 6.333333 0.5662463          15 snow_sand                  6.733333 0.5114561          15 snow_snow                  7.333333 0.5989409          15 snow_wood                  5.066667 0.7713110          15  alpha: 0.05 ; Df Error: 84  Critical Value of Studentized Range: 4.124617   Comparison between treatments means                                Difference   pvalue sig        LCL      UCL snow_gravel - snow_dry_leaves  1.9333333 0.232848     -0.5889913 4.455658 snow_metal - snow_dry_leaves   1.4000000 0.588616     -1.1223246 3.922325 snow_sand - snow_dry_leaves    1.8000000 0.307012     -0.7223246 4.322325 snow_snow - snow_dry_leaves    2.4000000 0.071587   . -0.1223246 4.922325 snow_wood - snow_dry_leaves    0.1333333 0.999987     -2.3889913 2.655658 snow_gravel - snow_metal       0.5333333 0.989528     -1.9889913 3.055658 snow_gravel - snow_sand        0.1333333 0.999987     -2.3889913 2.655658 snow_snow - snow_gravel        0.4666667 0.994348     -2.0556579 2.988991 snow_gravel - snow_wood        1.8000000 0.307012     -0.7223246 4.322325 snow_sand - snow_metal         0.4000000 0.997266     -2.1223246 2.922325 snow_snow - snow_metal         1.0000000 0.855987     -1.5223246 3.522325 snow_metal - snow_wood         1.2666667 0.687424     -1.2556579 3.788991 snow_snow - snow_sand          0.6000000 0.982179     -1.9223246 3.122325 snow_sand - snow_wood          1.6666667 0.393171     -0.8556579 4.188991 snow_snow - snow_wood          2.2666667 0.103505     -0.2556579 4.788991 When is a clause not essential? I am having trouble figuring out when to use commas to set off &quot;nonessential&quot; information.  Sometimes it's obvious:  Bob, who is thirty years old, is an alcoholic.  But other times I'm not sure:  The day he quits drinking * he will start a llama farm He has his heart set on owning El Duderino ranch * in New Mexico.  In the first case, my ear says that there should be a comma at *, even though information before it seems essential to me.  In the second case, the stuff after * is not essential, and yet it seems a little much to use a comma. Even that last sentence I wrote confuses me.  &quot;In the second case&quot; seems essential but I used a comma.  Is this correct? Does it depend on personal style and the length of the clause?  Or perhaps I'm misinterpreting the meaning of &quot;essential&quot; in this context? How to find a global minimum for $\frac{1}{2}x^tQx-b^tx$ Users lookup in chat search breaks with JavaScript error When using the  and trying to filter by user, I get this after typing several letters:        Two letters work fine, third or fourth letter breaks the lookup.  Can this please be fixed? Exporting 2D vector graphic from ArcScene to Illustrator How can I export 2d vector graphic from ArcScene so I can edit it with Adobe Illustrator? I've tried changing the options when I export 2D scene as AI file or PDF file, but they always remain as a unique image that does not allow me to edit the lines and polygons.