# robjohn

West Hills, CA

none

Age: 56

The Mean Square
(with one standard deviation and several unusual ones)

aka Rob Johnson

$\LaTeX$ support for Chat

 5h answered How to calculate $\lim_{n \to \infty}\sqrt[n]{\frac{2^n+3^n}{3^n+4^n}}$ 5h comment How do you factor $x^3-3x^2-4x+12$I noted that plugging in $x=2$ gives $0$. Divide by $x-2$ and the rest should be easy. 6h revised Deriving the formula of the Surface area of a sphereadd an explanation of the problem in the question 6h answered Deriving the formula of the Surface area of a sphere 7h comment Proving that $C$ is a subset of $f^{-1}[f(C)]$@BrianM.Scott: I have added my answer to a question recently marked as a duplicate of this one. If you feel it is too similar to yours, I will remove it. 7h answered Proving that $C$ is a subset of $f^{-1}[f(C)]$ 7h revised Can I try to tell experienced users not to answer bad questions?remove repetetive grammar 7h revised Can I try to tell experienced users not to answer bad questions?change the beginning to read as an appreciation rather than an endorsement 10h comment Can I try to tell experienced users not to answer bad questions?@BillDubuque: I am not recommending that sort of comment; however, I don't see any reason to repress someone's opinion, if politely expressed. Comments are ephemeral and if they are rude or not constructive, they can be removed. 10h revised Can I try to tell experienced users not to answer bad questions?fix typo 10h comment Can I try to tell experienced users not to answer bad questions?@quid: I have prefaced my post with something that is hopefully more addressed to the question and ties what I have said after into that. 10h revised Can I try to tell experienced users not to answer bad questions?try to more closely answer the question and tie what I have said to that 11h comment Can I try to tell experienced users not to answer bad questions?@quid: I said that bad questions should be closed. However, how one communicates that to people who have answered is a tougher question. My opinion about what is or is not a bad question may help explain the responses they might get to such a comment as they are suggesting. 11h comment Can I try to tell experienced users not to answer bad questions?As the only context for what a bad question is is given in the cited question, and that question talks about the missing context criteria, I felt it appropriate to mention context and its relation to bad questions. 11h revised Can I try to tell experienced users not to answer bad questions?fix the chronology 11h answered Can I try to tell experienced users not to answer bad questions? 11h comment If $u_{n+1}\le u_n+u_n^2$ and $\sum u_n$ converges, prove that $\lim\limits_{n\to +\infty}(n\cdot u_n)=0$@Lord_Farin: then, I noticed that $u_{n+1}\le u_n(1+u_n)$ has two cases: $u_{n+1}\le u_n$ and $u_{n+1}\ge u_n$ where $u_{n+1}\le u_n(1+u_{n+1})$. Either one gives $u_n\ge\frac{u_{n+1}}{1+u_{n+1}}$. 12h comment If $u_{n+1}\le u_n+u_n^2$ and $\sum u_n$ converges, prove that $\lim\limits_{n\to +\infty}(n\cdot u_n)=0$@Lord_Farin: actually, I started by solving $u_n^2+u_n-u_{n+1}=0$ for $u_n$. The solution is $$u_n= \frac{-1+\sqrt{1+4u_{n+1}}}2= \frac{2u_{n+1}}{1+\sqrt{1+4u_{n+1}}}\ge \frac{u_{n+1}}{1+u_{n+1}}$$ Then, seeing the final result, I knew I could avoid the whole quadratic formula sidetrack by using $\frac{x}{1+x}$. 12h comment Adding two discrete distributionsTrue; $Z$ is defined on the residue classes mod $10$ while $X$ is defined on $\{0,1,2,3,4,5,6,7,8,9\}$. However, there is a canonical, measure-preserving isomorphism between them. 19h comment Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$It might help to see the roots to note that $s^3+3s-4=(s^2+4)(s-1)$.