hofmeister
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 Jan 9 awarded Notable Question Oct 6 awarded Popular Question May 4 awarded Notable Question Mar 5 awarded Popular Question Sep 8 awarded Popular Question Jan 16 awarded Yearling Aug 28 accepted Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ Aug 28 comment Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ Don't know :). I thought thats the way. In the results from the exercises, nowhere is a $x$. If I keep the $x$ everything is fine? Sorry for editing. Aug 28 comment Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ Pleas also see my Summery. I really want understand the stuff! Aug 28 revised Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ added 299 characters in body Aug 28 comment Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ I did nearly the same as Legendre. Is it not correct because I missed the $x$? Why did I used an incorrect hybrid? I just did $$\frac{1}{(n+2) \cdot 3{n+2}} \cdot \frac{(n+1) \cdot 3^{n+1}}{1}$$. I’m really sorry to be slow off the mark.. Aug 28 comment Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ Ok. I asked because I’m a little bit confused. In my formulary is written: $r = \lim\limits_{n \to \infty} \left| \frac{a_n}{a_{n+1}} \right|$. In the exercises from the institute they use: $\lim\limits_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|$. I used the second way. I’m quite aware where’s the different. With the second way I get the value for which the $\left| x \right|$ the power series is convergence, right? Aug 28 comment Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ So I have to inverse the result? Aug 28 asked Power series: Is the radius of convergence $\frac{1}{3}$ for $\frac{x}{1\cdot3} + \frac{x^2}{2\cdot3^2} + \frac{x^3}{3\cdot3^3}+…$ Aug 28 revised Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? edited title Aug 28 comment Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? Thanks very much. I will keep in my mind. Wish a nice day. Aug 28 revised Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? deleted 1 characters in body Aug 28 accepted Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? Aug 28 revised Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? added 1 characters in body Aug 28 revised Why $\lim_{n \rightarrow \infty}\frac{(5n^3-3n^2+7)(n+1)^n}{n^{n+1}(n+1)^2} =5e$? edited body