If $\lim_{n\to\infty}a_{n}=l$, Then prove that $\lim_{n\to\infty}\frac{a_{1}+a_2+\cdot..+a_n}{n}=l$
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means
How to get world-space matrix of any pose bone? Is there a command for getting world-space matrix of pose bones, same as obj.matrix_world for objects? I found pose_bone.matrix, but it gives weird result for me. Statistical saturation attack on block ciphers I was wondering if anyone around here could give me some explanation on this type of attacks. Pretty much the only thing that I could find is .  What I really need is basic explanation of the attack itself with a small example if possible such as any basic block cipher that you could come up with with 3-4 rounds. This is for my personal understanding so any input is more than welcome. What does the Asterisk * mean in Objective-C? For example, when I type ping 8.8.8.8 &amp;, why can we see ping process working? And when I type find / -name '*test*' &amp; , it's also seen on monitor.  Why is that? Is it not really in background? A required field that isn't really required? ...the email field in my clients data entry system is required but users of the system are allowed to enter na@na.com if the customer refuses or doesn't have an email address. Is this best practice? Have any suggestions or workarounds for their solution? How does one find which files are taking up 80% of the space on a Linux webserver? The drive is constantly filling up. You've hunted down all the spare and random files you can. grep'd for coredump files and even removed some of the un-needed backups...  What would be your next move.  The actual server in question has 10GB of website files and the OS shouldn't take any more than 10GB so how do you track down what's filling a 50GB (virtual) drive? Join CSV file to shapefile File permissions and saving Original sentence:     Prince Andrew, looking again at that genealogical tree, shook his head, laughing as a man laughs who looks at a portrait so characteristic of the original as to be amusing.    (War and Peace, Tolstoy, English translation)     In the sentence above, shouldn't the comma before laughing be omitted if this is about the participle clause denoting "an action that happens at the same time in the past"?  I mean it should be      Prince Andrew…shook his head laughing as a man…   Plus, shouldn't the verb laugh after a man be in the past tense in order to be in accordance (agreement) with shook his head?   You know, the whole sentence should be consistent…. When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: "... the birthday of your youngest." [implying her child]  She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the comparative must be used instead: "... the birthday of your younger child."  She was adamant that this was a solid grammatical rule that she was taught throughout her education.  As a younger Briton, I have relatively little formal grammatical education to older people who were better taught in this regard, so I usually defer to her on grammatical rule knowledge.  Is she right?  Are superlatives not permitted when the domain of the object is only two?  To me it seems bizarre.  The minimum or maximum of any set does not only exist when there are different minima and maxima, or indeed something which is neither. Upon system restart, dconf editor doesn't save changes I can use the dconf-editor to change my touchpad settings to natural scrolling, but upon system restart the settings get reverted. (But not on sleep or hibernate.) When I open the editor, the option is still orange indicating it has been changed. when I uncheck and recheck the natural scroll option, it is re-enabled. Is there a fix, or am I changing the wrong option? The path is org > gnome > settings-daemon > peripherals > touchpad > natural-scroll.  Currently running 13.10 C# regex pattern to extract urls from given string - not full html urls but bare links as well What are the drawbacks with using UUID or GUID as a primary key? I would like to build a distributed system. I need to store data in databases and it would be helpful to use an  or a  as a primary key on some tables. I assume it's a drawbacks with this design since the UUID/GUID is quite large and they are almost random. The alternative is to use an auto-incremented INT or LONG.  What are the drawbacks with using UUID or GUID as a primary key for my tables?  I will probably use Derby/JavaDB (on the clients) and PostgreSQL (on the server) as DBMS. What would be the sum of the following series?  $$\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$$  Thanks How do I calculate the determinant of the following $n\times n$ matrices  $$\begin {bmatrix} 0 &amp; 1 &amp; \ldots &amp; 1 \\ 1 &amp; 0 &amp; \ldots &amp; 1 \\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ 1 &amp; 1 &amp; ... &amp; 0 \end {bmatrix}$$  and the same matrix but one of columns replaced only with $1$s?  In the  above matrix all off-diagonal elements are $1$ and diagonal elements are $0$. In the begining of "" episode (Star Trek Next Generation 6x16) an Yridian tells Worf, that he has a certain information,      that Worf's father is still alive (apparently not killed in ) and is held in a prison camp on Carraya IV.   Yridian is an information broker and agrees to reveal details (i.e. location) only for a price.      Worf agrees.   How or with what Worf would pay for this? There is no economic factor inside the Federation (no money is being used) and I don't recall anything, Worf would have on board Enterprise, that would have enough value for an information this kind. Getting the location from an IP address I want to retrieve information like the city, state, and country of a visitor from their IP address, so that I can customize my web page according to their location. Is there a good and reliable way to do this in PHP? I am using JavaScript for client-side scripting, PHP for server-side scripting, and MySQL for the database. How do I use F3 to get my coordinates when my laptop makes F3 a special key? A pitcher contains $X + 1$ blue balls and $Y + 1$ red balls. It is known that $X, Y$ are independent random variables, and it is given that $X \sim \mathrm{Poisson}(n), Y \sim\mathrm{Poisson}(2n)$. Calculate the limit: $\displaystyle\lim_{n\to \infty}\mathbb P (X + n = Y) $   I tried to condition on the value of $Y$ and to use the Law of total probability but it did not lead to a solution. ( I tried to sum: $ \sum_{i=0}^\infty\mathbb P(X+n=Y|Y=i)\mathbb P(Y=i) $ and get an expression that I can calculate its limit as n goes to infinity) We  that there's a difference in meaning between try used with the infinitive and  try used with the gerund:     I tried sending her flowers. (Meaning: An experiment: I sent her flowers to see what will happen).   I tried to send her flowers. (Meaning: I tried to go through the procedure necessary to send flowers to her. The procedure might have been difficult.)   (per Michael Swan's PEU, Unit 299.6)   Will the same distinction hold if we use trying:     A man is trying setting up a password on his computer. (Is he experimenting, wanting to see what will happen?)   A man is trying to set up a password on his computer. (Is he trying to go through all the necessary steps, probably difficult, of setting up a password?)