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robjohn's user avatar
robjohn's user avatar
robjohn
Moderator
  • Member for 14 years, 9 months
  • Last seen this week
  • West Hills, CA
678 votes
Accepted

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

177 votes
Accepted

What's 4 times more likely than 80%?

155 votes

Slice of pizza with no crust

154 votes

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

132 votes
Accepted

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

106 votes

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

95 votes

Is there any integral for the Golden Ratio?

94 votes
Accepted

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

90 votes
Accepted

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

84 votes
Accepted

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

79 votes

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

78 votes
Accepted

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

78 votes

Can an infinite sum of irrational numbers be rational?

73 votes
Accepted

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

70 votes

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

69 votes

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

69 votes

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

68 votes

Trivial zeros of the Riemann Zeta function

68 votes

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

64 votes
Accepted

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

61 votes
Accepted

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

58 votes
Accepted

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

58 votes
Accepted

Question about a rotating cube?

57 votes

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

56 votes

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

56 votes

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

56 votes

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

54 votes
Accepted

Equation of a "tilted" sine

53 votes

Coin flipping probability game ; 7 flips vs 8 flips

52 votes

Curious Integral Proof

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