User robjohn - Mathematics Stack Exchange

678 votes

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How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

answered Oct 23, 2011 at 17:26

177 votes

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What's 4 times more likely than 80%?

answered Aug 12, 2013 at 12:25

155 votes

Slice of pizza with no crust

answered Sep 1, 2013 at 23:54

154 votes

How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?

answered Dec 24, 2014 at 20:44

132 votes

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Parabola is an ellipse, but with one focal point at infinity

answered May 2, 2014 at 12:53

106 votes

Is it possible to represent every irrational number as a (limit of) an infinite sum of rational numbers?

answered Oct 6, 2015 at 6:29

95 votes

Is there any integral for the Golden Ratio?

answered Feb 14, 2016 at 14:33

94 votes

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Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

answered Sep 20, 2013 at 15:35

90 votes

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Arc length contest! Minimize the arc length of $f(x)$ when given three conditions.

answered Feb 4, 2015 at 1:44

84 votes

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Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series.

answered Mar 4, 2012 at 3:30

79 votes

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

answered Sep 3, 2012 at 1:18

78 votes

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In which cases is the inverse of a matrix equal to its transpose?

answered Jun 10, 2012 at 23:36

78 votes

Can an infinite sum of irrational numbers be rational?

answered Feb 9, 2016 at 14:04

73 votes

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Is it possible to write a sum as an integral to solve it?

answered Nov 3, 2014 at 14:00

70 votes

I have a problem understanding the proof of Rencontres numbers (Derangements)

answered Nov 18, 2011 at 20:53

69 votes

Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$

answered Jun 19, 2012 at 15:29

69 votes

Are all limits solvable without L'Hôpital Rule or Series Expansion

answered Jun 24, 2015 at 12:54

68 votes

Trivial zeros of the Riemann Zeta function

answered Nov 23, 2016 at 17:55

68 votes

To sum $1+2+3+\cdots$ to $-\frac1{12}$

answered Jan 9, 2014 at 18:14

64 votes

Accepted

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

answered Aug 17, 2013 at 14:34

61 votes

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A closed form of $\int_0^\infty\frac{\sqrt[\phi]{x}\ \arctan x}{\left(x^\phi+1\right)^2}dx$

answered Oct 9, 2013 at 19:37

58 votes

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How to evaluate $\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$

answered Mar 15, 2013 at 13:45

58 votes

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Question about a rotating cube?

answered Mar 2, 2012 at 22:36

57 votes

How to prove a trigonometric identity $\tan(A)=\frac{\sin2A}{1+\cos 2A}$

answered Mar 29, 2012 at 22:23

56 votes

Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.

answered Oct 31, 2011 at 17:42

56 votes

Linear diophantine equation $100x - 23y = -19$

answered Sep 27, 2011 at 20:22

56 votes

Why is $i^3$ (the complex number "$i$") equal to $-i$ instead of $i$?

answered Dec 18, 2013 at 9:29

54 votes

Accepted

Equation of a "tilted" sine

answered Sep 16, 2017 at 14:23

53 votes

Coin flipping probability game ; 7 flips vs 8 flips

answered Jan 31, 2014 at 10:44

52 votes

Curious Integral Proof

answered Sep 3, 2013 at 3:57

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7,322 Answers

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

What's 4 times more likely than 80%?

Slice of pizza with no crust

How to prove that $\frac{\zeta(2) }{2}+\frac{\zeta (4)}{2^3}+\frac{\zeta (6)}{2^5}+\frac{\zeta (8)}{2^7}+\cdots=1$?

Parabola is an ellipse, but with one focal point at infinity

Is it possible to represent every irrational number as a (limit of) an infinite sum of rational numbers?

Is there any integral for the Golden Ratio?

Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

Arc length contest! Minimize the arc length of $f(x)$ when given three conditions.

Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series.

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

In which cases is the inverse of a matrix equal to its transpose?

Can an infinite sum of irrational numbers be rational?

Is it possible to write a sum as an integral to solve it?

I have a problem understanding the proof of Rencontres numbers (Derangements)

Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$

Are all limits solvable without L'Hôpital Rule or Series Expansion

Trivial zeros of the Riemann Zeta function

To sum $1+2+3+\cdots$ to $-\frac1{12}$

Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$

A closed form of $\int_0^\infty\frac{\sqrt[\phi]{x}\ \arctan x}{\left(x^\phi+1\right)^2}dx$

How to evaluate $\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$

Question about a rotating cube?

How to prove a trigonometric identity $\tan(A)=\frac{\sin2A}{1+\cos 2A}$

Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.

Linear diophantine equation $100x - 23y = -19$

Why is $i^3$ (the complex number "$i$") equal to $-i$ instead of $i$?

Equation of a "tilted" sine

Coin flipping probability game ; 7 flips vs 8 flips

Curious Integral Proof