Arjang
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 18h comment Simplify triangular sum of triangular numbers: $\sum_{i=1}^{n}(\frac12i(i+1))$ yes, expand the product and sum, it is stupidly easy Jan 25 comment How to find the limit of a sum of reciprocals $\lim_{n\to\infty}(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n})$? Strange, duplicate elementary problems getting too much upvotes. Jan 25 comment How to find this limit : $\lim_{n \to \infty} \frac{2-\sqrt{2+\sqrt{2 +\sqrt{2+ \cdots n \text{ times}}}}}{4^{-n}}$ What have you tried? Where is this question from? Jan 24 comment Coefficient of $x^{50}$ in the expansion of $\prod_{n=1}^{52}{(x+n)}$ any hints on what you have tried, what about coefficints of $x^0,x^1,x^2$? Jan 24 comment The name of the sum $\sum_{i=0}^n \frac{1}{m-i}$ This is not a different series than finite harmonic series , since it can be written as difference of two harmonic series with different uppper index or just one harmonic series with lower index starting at higher number, Jan 22 comment Derivative of a vector with respect to a matrix Also, I like your thinking, just make it explicit as what the definition should be. Jan 22 comment Derivative of a vector with respect to a matrix That totally depends on definition being used. Jan 19 comment is this correct $\lim_{ n \to \infty} \sum_{k=2^n}^{2^{n+1}} \frac{1}{k}= \ln 2$? yes, now it is easy with your result. Jan 15 comment How many dots do I have to write? You wont be doing the dots, you will use \cdots tex, latex,mathjax as so $\cdots$ Jan 14 comment Example of two analytic functions that differ at countably infinity many point @CameronWilliams : is it even possible with the case analytic everywhere? I didnt think it would, but that is not a proof of course Jan 13 comment Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$? @mathjacks : updated my answer, I think you need to look athttps://en.wikipedia.org/wiki/Analytic_continuation Jan 12 comment How can an angle be negative? fyi angles can be complex or even matrix, now get somebody explain that cause I cant. Jan 10 comment Find the value of the infinite product $\sqrt\frac12\cdot\sqrt{\frac12+\sqrt\frac12}\cdot\sqrt{\frac12+\sqrt{\frac12+\sqrt\frac12}}\cdots$ i am not the down voter, but you can do few more steps in few different ways just to show yourself that you really have tried. Jan 9 comment example of a function that could only be defined recursively @mvw : my question is not about computing theory, for example factorial can be defined recursively or as gamma function, can it be shown that Ackerman fuction can not be defined without requiring it's own previous values ? Jan 7 comment example of a function that could only be defined recursively Hi Robert, I did not mean to ask a computing question, by recursive I mean something that uses a relation to self similarity in some way. Eg the next Fibonacci number is related to two previous fib numbers, yet it here is a function that generates all the fib numbers without relying on the knowledge of previous numbers. Similar thing for recursive definition of factorial works with gamma function. So it seems that although it might be difficult to have a recursive function defined non recursively with some effort, but is thee a case where it is impossible? Jan 7 comment example of a function that could only be defined recursively @NoChance look up gamma function Jan 7 comment example of a function that could only be defined recursively @NoChance not really, just multiply the numbers from 1 to n and you have the result. Even Fibonacci can be written as a function of 1 variables. Actually the multiplication of 1 to n is a better implementation of n! Than the recursive definition. The text books use n! As a bad example to introduction into recursion. Jan 5 comment How to find the sum of the infinite series whose general term is not easy to visualize this is not an answerable question Jan 5 comment How to find the sum of the infinite series whose general term is not easy to visualize The general term can be made anything we want it to be, this is same as given a finite sequence trying to guess the next term. without the explicit formula for the general term or some recursive way of defining the terms it is just waste of time to guess the general fprm. Jan 3 comment Behavior of interesting sequence can you give the calculation for few terms?