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robjohn

West Hills, CA

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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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Top Questions
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512
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
math.stackexchange.com

172
What's 4 times more likely than 80%?
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136
Slice of pizza with no crust
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119
How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?
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115
Parabola is an ellipse, but with one focal point at infinity
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95
Is it possible to represent every irrational number as a (limit of) an infinite sum of rational numbers?
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80
Arc length contest! Minimize the arc length of $f(x)$ when given three conditions.
math.stackexchange.com

80
Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
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78
Is there any integral for the Golden Ratio?
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71
Can an infinite sum of irrational numbers be rational?
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71
Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series.
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64
Is it possible to write a sum as an integral to solve it?
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61
Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
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58
A closed form of $\int_0^\infty\frac{\sqrt[\phi]{x}\ \arctan x}{\left(x^\phi+1\right)^2}dx$
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56
Why is $i^3$ (the complex number “$i$”) equal to $-i$ instead of $i$?
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54
Why does $1+2+3+\cdots = -\frac{1}{12}$?
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54
How to evaluate $I=\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$
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52
Coin flipping probability game ; 7 flips vs 8 flips
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52
Curious Integral Proof
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51
How to prove a trigonometric identity $\tan(A)=\frac{\sin2A}{1+\cos 2A}$
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49
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
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49
Find the simplest counterexample against exchanging limit and summation
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48
Why can the complex conjugate of a variable be treated as a constant when differentiating with respect to that variable?
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48
Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$
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47
Linear diophantine equation $100x - 23y = -19$
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47
Trivial zeros of the Riemann Zeta function
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46
How do you prove Gautschi's inequality for the gamma function?
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46
How many lists of 100 numbers (1 to 10 only) add to 700?
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45
Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$
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43
I have a problem understanding the proof of Rencontres numbers (Derangements)
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