robjohn

West Hills, CA

none

Age: 56

the mean square 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 sphere
add 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 distributions
True; $Z$ 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 $s^3+3s-4=(s^2+4)(s-1)$.
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