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

aka Rob Johnson

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11h
comment Find the value of this infinitely nested radical (it appears to obtain multiple values)
True. We simply need to map the points $\frac1{16}$, $0.073182744516454277369$, and $\frac{17}{16}$ to $\frac{255}{256}$, $0.994644285905039381396$, and $-\frac{33}{256}$.
12h
comment How find this limit $I=\lim_{n\to\infty}n^a\left(\int_{0}^{\pi/2}\sin{(nx)}\cos^n{x}dx\right)=b$
We miss you on chat :-( I hope your work is going well.
13h
comment How many zeroes are in 100!
would the downvoter care to comment?
13h
revised Find the value of this infinitely nested radical (it appears to obtain multiple values)
analyze the problem more completely
23h
revised Find the value of this infinitely nested radical (it appears to obtain multiple values)
note the stability of the fixed points
1d
comment Find the value of this infinitely nested radical (it appears to obtain multiple values)
The $\frac{17}{6}$ in your answer should be $\frac{17}{16}$
1d
answered Find the value of this infinitely nested radical (it appears to obtain multiple values)
1d
comment Does a bounded continuous function map Cauchy sequences to Cauchy sequences?
(+1) Good answer :-)
1d
answered Does a bounded continuous function map Cauchy sequences to Cauchy sequences?
1d
comment Limit of factorial function: $\lim\limits_{n\to\infty}\frac{n^n}{n!}.$
Something has to be wrong. The root test should give a limit of $1/e$ here. It appears that although the $n^\text{th}$ roots tend to $1$, there are an increasing number of them. This will balance to give $n/e$ in the numerator, not $1$.
1d
comment Limit of factorial function: $\lim\limits_{n\to\infty}\frac{n^n}{n!}.$
@ianks: It might help to note that $$\frac{(n+1)^{n+1}}{(n+1)!}=\frac{(n+1)^n}{n!}$$ Then divide that by $$\frac{n^n}{n!}$$
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
I've undeleted since Random Variable points out that I did use a different contour (however slightly different).
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
@RandomVariable: yes, I did that, too. I guess I could be convinced to undelete it ;-)
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
The answer is accurate (+1), but it would really be nice to see more verbal explanation to your answers. Just a mention that you are integrating by parts 4 times would be helpful. Such a terse answer is sometimes hard to follow.
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
@RandomVariable: I don't think my approach is any different, now that I look more closely at yours. I should just delete mine.
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
Shoot... now that I look at this, I think this may be the same as RandomVariable's approach except that I moved $\frac{z^3}{z^5}$ to the lower contour.
1d
answered Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
1d
comment Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx $ using contour integration
So is there no question left? I don't see one.
1d
answered Limit of factorial function: $\lim\limits_{n\to\infty}\frac{n^n}{n!}.$
1d
comment How to show if A is denumerable and $x\in A$ then $A-\{x\}$ is denumerable
@AsafKaragila: you'd be the one I'd ask about that, so I won't question :-)