Is there a Relationship between sum and sum of reciprocals? Is there any relationship between the sum of positive numbers and the sum of the reciprocals of the same numbers? For example:  $A=1+2+3.5$ and $B=1+1/2+ 10/35$  Thanks!
Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$ If we knew $\sum_{i=1}^{n} f(i)=S$  ($n$ can be $\infty$), is there anything we could say about $\sum_{i=1}^{n} \dfrac {1}{f(i)}$ in terms of $S$?  The only thing I was able to find on the web is . If there is no known relationship, is it possible for there to exist one that we just haven't discovered?
Advantages of parallel over serial connections As far as my understanding goes, parallel data connections are faster than serial at the same frequency. However, when you increase the frequency in parallel you start getting bits 'cross-talking' and getting transferred onto the next bus. Serial however, since it's only a single bus line, can have the frequency increased to make it faster than parallel without a problem. Also, surely parallel is more expensive as it uses more lines.  So my question is, what actually is the benefit of using a parallel data connection over a serial one? Are there any? If not, why do we still use parallel connections? I have three different 1024-bit public keys with common exponent $e$ but different moduli. A message $m$ is encrypted (without padding) using the three keys, which results in three different encrypted messages.  Given the three pairs of public keys $(N_i,e)$ and the encrypted messages $c_i=m^e\bmod N_i$ , how do I decipher the original message $m$ ? I have a small utility that I use to download an MP3 file from a website on a schedule and then builds/updates a podcast XML file which I've added to iTunes.  The text processing that creates/updates the XML file is written in Python. However, I use wget inside a Windows .bat file to download the actual MP3 file. I would prefer to have the entire utility written in Python.  I struggled to find a way to actually download the file in Python, thus why I resorted to using wget.  So, how do I download the file using Python? Is there a way to specify fragile mode as default for all frames? Now I know how to define a fragile frame: \begin{frame}[fragile]. Prove that a set in $\mathbb R^3$ is not an algebraic set I want to prove that the set $\{(\cos(t),\sin(t),t)\in A^3(\mathbb R); t\in \mathbb R \}$ is not an algebraic set.   I already proved that the set $\{(\sin(t),t)\in A^2(\mathbb R);t\in \mathbb R \}$ is not algebraic but the method that I used doesn't seems to be general. Travelling with two different passports I was just wondering if you have two passports (a Chinese one and an Australian one), and you booked your airline ticket with the Chinese one, will you have to show both of your passports or just one?  The thing is, on my Chinese passport, it has my birth name, but then when I became an Australian citizen, I legally removed my Chinese name and replaced it with my English name. So I don't know whether I should just show the passport officials the one that I booked the airline ticket with. Convert month name to month number in SQL Server How do I tell what version and edition of Windows is on the filesystem? MySQL Error 1093 - Can't specify target table for update in FROM clause I have a table story_category in my database with corrupt entries. The next query returns the corrupt entries:  SELECT *  FROM  story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category INNER JOIN         story_category ON category_id=category.id);   I tried to delete them executing:  DELETE FROM story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category        INNER JOIN story_category ON category_id=category.id);   But I get the next error:      #1093 - You can't specify target table 'story_category' for update in FROM clause    How can I overcome this? converge and converge absolutely of a series $f(x)$ is a continuos fuction in $[0, 1]$ and differentiable twice on $0$.  $U_n=(-1)^{n}f(\frac{1}{n})$. I need to prove that:   $1.$if $\sum_{n=1}^\infty U_n$ converge then $f(0)=0$.  $2.$if $f(0)=f'(0)=0$ then $\sum_{n=1}^\infty U_n$ converge absolutely.  Now, from the detail that $f(x)$ is differentiable twice on $0$ I think I need to write $f(1/n)$ with Maclaurin series with 2 degree but it doesn't work very nice. can you guide me please? thanks! How can I get multiple stacked plots (ybar stacked, stack plots=y) in one diagram, such that there are multiple stacked bars for the same x-coordinate, each slightly shifted? Is there a way to reset pgfplot's zero levels after an \addplot command, such that the next \addplot[xhshift=...] doesn't add something to the current stack, but rather starts a fresh stack?  FWIW, overlaying two plots with scale only axis won't help; I need this to work with groupplot Classify all groups with order $pq$, $p$ is not equal to $q$ I am reading the following material:  . At page 5, there is a proof classifying all groups with order $pq$(they are all primes and $p$ is not equal to $q$). I am lost in the last two sentence, which claims the semidirect product are all isomorphic. Could someone help me to understand it? Thanks! I recently made changes to my fstab file and, upon reboot, noticed I had an error in it. I get the typical mount error on boot. I went to try and modify it by entering the read-only mode but then, since it's read only, I can't access it. Is there a way around this or some way to delete the file so I can use the backup (which I'm pretty sure works)? Does anyone know if there are any video formats (besides the HUGE uncompressed avis) that you can render in that maintain the alpha channel? (i.e. for after FX etc.)   I used to use quicktime, but that's no longer an option.  I know you can render in png. or other image formats, but video is significantly smaller, and I often work on machines with less space &amp; resources. What is the most efficient way to add rows and columns to a matrix? Can we denied permission for synchronized data extension in Salesforce Marketing Cloud, My requirement is, I don't want to allow users to access synchronized data extension either in contact builder or in Subscribers. Why didn't the basilisk bite in Chamber of Secrets destroy the Horcrux? As the title asks, why didn't the basilisk bite received in the Chamber of Secrets destroy the Horcrux inside the bitten person?   Yes, I know Fawkes quite quickly healed the bite wound with his phoenix tears, but when Harry used the basilisk fang to destroy Tom Riddle's diary the destruction of that Horcrux was immediate. When Ron hit the locket with the Sword of Gryffindor, it was destroyed immediately. Although the destruction of the ring occurred off-page, Dumbledore used the Sword of Gryffindor to destroy it, so presumably, like the locket, it was gone right away. Nagini died straightaway when Neville decapitated her. The destruction of the Hufflepuff cup happens off-page. The diadem seems to have been destroyed by Fiendfyre immediately as well, as when Harry examined it outside the Room of Requirement it was already leaking a blood-like substance, and then it cracked in half. When Voldemort hit Harry with Avada Kedavra in the forest, Harry woke up in limbo with the last fragment of Voldemort's soul - that awful flayed baby-like being - separated from him immediately.   Is there a logical/canon-based explanation for why the fragment of Voldemort's soul residing in Harry wasn't destroyed upon Harry being bitten by the basilisk?  NOTE: I've read the HP Wiki's entry on Horcruxes; however, I find the HP Wiki to be inconsistent in its accuracy, so I'm hesitant to accept the Wiki's explanation on the matter. I'd prefer an explanation constructed from information in the books or a statement by JKR, or the like. How to check if a macro value is empty or will not create text with plain TeX conditionals? I have a macro which holds some text value, e.g. \macro{some text}. If it is empty, I would like for nothing to appear in the document, but it has some content of any kind which would produce text displayed in the document, I would like a message to appear, "Text: some text".   \macro{} would be considered empty. \def\somedata{}, \macro{\somedata} would be considered empty. \macro{0} would be considered not empty.   I have tried making a TeX conditional which can check if the value is not empty, but nothing I tried works, e.g.:  \ifx #1 {} \else     Text: #1 \fi  \ifx#1{} \else     Text: #1 \fi  \ifx #1 \nil \else     Text: #1 \fi  \ifx#1!="" \else     Text: #1 \fi   What is the correct syntax for creating a conditional in plain TeX with checks if a value is not empty? Drawbacks of making public which journal a manuscript is submitted to, while it is under review? Many researchers list out their submitted manuscripts on their website. Some specify the journal name, like     Smith J, Oliver J (under review) My awesome paper. Nature.   while others don't, like     Smith J, Oliver J (under review) My awesome paper.   One reason I can think of as to why some don't mention the journal name is that they may get embarrassed in the case where the current journal rejects the paper. Then, the "circle" will know this paper gets rejected from Nature first and then ends up in an inferior journal.  Besides this, are there any other considerations preventing people from mentioning to which journal they submit a paper to?  P.S.: I am asking because my advisor is a researcher who only mentions accepted  papers on his webpage. As a student hunting jobs, I feel it is advantageous for me to mention my submitted papers on my webpage. I hesitate to do so, as I worry I may make my advisor unhappy by announcing in which journal our papers are currently under review. What is the difference between buy and purchase