Give an example of a series such that $\sum a_n$ is convergent but $\sum a_{3n}$  is divergent.  I am trying to construct an example such that $\sum a_n$ is convergent but $\lim a_{3n}$ is not zero. But I could not find such example. Give me some hints.
Give an example of a convergent series $$\sum_{n=1}^{\infty}a_n$$ such that the series $$\sum_{n=1}^{\infty}a_{3n}$$ is divergent..  I cannot find find any kind of series... I am also be very thankful if you find a divergent series (changing the term convergent)...
Database files that are built using SQL 2008 are not compatable with 2005. Is there a work around? I am currently in the process of trying to repair a power supply that has had one of its DC rails fail. A resistor in the PSU has exploded and I am trying to find what value it is.    Band 1: White Band 2: Brown Band 3: Silver (Possibly Grey?) Band 4: Gold Band 5: Green    The weird thing is that the middle band appears to be silver, which should be invalid as far as I can tell. If you assume the silver is grey (although this is unlikely, as there still needs to be a grey colour as well and the band is metallic), it produces a value of resistor which is incredibly uncommon to the point it does not exist (91.8 Ohms 0.5%).  Apologies for the noobie question, I'm just stumped after hours of trying to understand why this is and coming up short :). What are the assumptions for applying a quantile regression model? The question has been asked (one time) on CV before, but the answer is really imprecise and does not really answer the question in my opinion.  So: What are the assumptions for estimating a linear regression model via quantile regression?  To my understanding (and as several CV users have mentioned), quantile regression does not assume any specific distribution of the error terms - does that mean that, in a time series model, autocorrelation and heteroscedasticity do not have to be accounted for?  What about the other Gauss-Markov assumptions? I would assume that the assumption of no perfect multicollinearity has to be met when applying quantile regression, but do the parameters have to be linear? The linearity assumption only has to hold for the specific quantile I would assume.  Anyways - I do not find any backup for any of my thoughts in the scientific literature and I would appreciate a comprehensive answer. Thank you! Imagine that you want to develop a non-trivial end-user desktop (not web) application in Python. What is the best way to structure the project's folder hierarchy?  Desirable features are ease of maintenance, IDE-friendliness, suitability for source control branching/merging, and easy generation of install packages.  In particular:   Where do you put the source? Where do you put application startup scripts? Where do you put the IDE project cruft? Where do you put the unit/acceptance tests? Where do you put non-Python data such as config files? Where do you put non-Python sources such as C++ for pyd/so binary extension modules? Sequences in $C(X)$ converging uniformly implies uniform boundedness and equicontinuity Let $X$ be a metric space and let $\{ f_n \}_{n \geq 1}$ be a sequence in $C(X)$. Show that if $\{ f_n \}_{n \geq 1}$ converges uniformly on $X$ then $\{ f_n \}_{n \geq 1}$ is both uniformly bounded and equicontinuous.  Could I get a hint? "whatever" as pure determiner? My dictionaries and references define, and I've always thought of, one of the functions of the word whatever as a "relative determiner."  In a sentence like, "I will help you in whatever way is possible,"  inserting the relative pronoun "that" between "way" and  "is", or replacing "whatever" with "the" - a pure, non-relative determiner - (I reckon) renders it ungrammatical:     *I will help you in whatever way that is possible.   *I will help you in the way is possible.   However, I do often encounter utterances like the first one above, such as:     My hope and intent is to contribute in whatever way that I can.   I wish to be of service to the local communities in whatever way that is possible.   where "that" is used, and thus "whatever" can be replaced by "the" without  making the sentences ungrammatical (if they are grammatical to begin with):     My hope and intent is to contribute in the way that I can.   I wish to be of service to the local communities in the way that is possible.   Is this usage of "that" with "whatever" wrong, though colloquial? How do I see that every left ideal of a square matrix ring over a field is principal? As the question title suggests, how do I see that every left ideal of a square matrix ring over a field is principal? How do I find out which program and process ID accesses a given IP address in Windows? Is it possible to catch, which program is accessing a specific IP address?   I found my computer is flooding and wish to check addresses one by one.  May be it is possible to set up some audit for this? App drawer icon gone from Cyanogenmod dock I have a Samsung Galaxy S2, running the latest CM10.1.  I lost the app drawer icon on my Dock; I must have deleted it. The app drawer icon lets you go to the app list, and the widget list.  How do I get the app drawer icon back? The icon looks like a circle with 6 dots inside it. I would like to align the view straight on to a face, perpendicular to the normal. How do I align the 3D viewport to the face of a mesh? Is string in array? What would be the best way to look in a string[] to see if it contains a element. This was my first shot at it. But perhaps there is something that I am overlooking. The array size will be no larger than 200 elements.  bool isStringInArray(string[] strArray, string key) {     for (int i = 0; i &lt;= strArray.Length - 1; i++)         if (strArray[i] == key)             return true;     return false; } What is "angle of view" in photography? I read on the :     Focal-length determines the angle-of-view seen through a lens for a   given sensor-size. With a full-frame sensor a lens gives the same   angle-of-view as it would on a 35mm film camera. With a smaller   sensor, the angle-of-view becomes smaller. The crop-factor, also   called FLM, is the ratio representing the difference in equivalent   focal-lengths. So a 150mm on a full-frame DSLR such as the Nikon D700   gives the same angle-of-view as a 100mm on a D7000 since its FLM is   1.5X.      Short focal-lengths show a greater angle-of-view compared to longer   ones. [...]   In layman's terms, what is angle-of-view? Is it the same as focal length? If not, how is it different? How is it used? Why do I need to know about it? Logistic regression vs. LDA as two-class classifiers Difference between static class and singleton pattern? I'm currently writing an import script/addon.  The file format is one vertex per line: x, y, z, u, v With 3 lines for each triangle (no quads).  So far I've got vertex's, edges and faces all importing correctly.  Now I just need to import the UV coordinates for each vertex.  However I'm having trouble trying to find a way to do this.  The best result so far was copying code from the UV operator template, which gave me a UV Map, but it puts the whole model at one point. Name of short sci-fi story involving a musician who is punished for listening to Bach I have a shape (rounded rectangle) in PowerPoint 2007 of which I would like to increase the vertical size only (to illustrate de-bottlenecking). So, the width will stay the same but the height will grow (both from the top and bottom, so the centre will remain in the same location).  Custom Animation -> Emphasis only appears to change the whole shape.  Is it possible to increase only the vertical size (stretch the shape)?  This is during animation of the shape. Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$ Is it possible to choose which OS will be loaded using a hardware switch? Media keys not working for iTunes (pause/play, skip buttons)