User Amihai Zivan - Mathematics Stack Exchange

52 votes

9 answers

37k views

Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?

asked Jul 13, 2012 at 13:28

28 votes

20 answers

3k views

Interesting Math for 3-graders

asked Jun 23, 2013 at 14:23

11 votes

3 answers

3k views

Construction of a right triangle

asked Oct 8, 2012 at 17:04

10 votes

1 answer

383 views

What's the name of this quantity?

asked Dec 31, 2013 at 19:17

9 votes

6 answers

2k views

dissection of a $1\times 5$ rectangle to a square

asked Jan 5, 2012 at 22:40

7 votes

1 answer

473 views

Approximating Increasing Sequence

asked Dec 11, 2012 at 22:04

7 votes

2 answers

326 views

If $\sum\limits_{k=1}^{\infty}a_k=S $, then $ a_4+a_3+a_2+a_1+a_8+a_7+a_6+a_5+\dots=?$

asked Jun 17, 2012 at 13:42

6 votes

3 answers

554 views

Evaluating $\frac{1}{\sqrt{4}+\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}+\sqrt{16}}+\frac{1}{\sqrt{16}+\sqrt{20}+\sqrt{25}}=?$

asked Jun 22, 2012 at 12:30

4 votes

0 answers

244 views

Is it a "paradox", or a flaw in the question?

asked Dec 3, 2014 at 8:52

3 votes

6 answers

234 views

Proving that $\int_0 ^1 \frac{\text{d}s}{\sqrt{1-s^2}}$ converges with no trig functions

asked Dec 19, 2014 at 13:56

3 votes

2 answers

5k views

Elementary proof for $\text{rank} \left(A \otimes B \right) = \text{rank}A\cdot \text{rank}B$

asked Mar 10, 2014 at 19:13

3 votes

1 answer

73 views

Proof for $\forall x$, $\exists y$ s.t $1/2 \le |x-y|\le 1$ and $ |\cos \pi x - \cos \pi y|\ge 1$

asked Jul 2, 2014 at 14:09

3 votes

2 answers

129 views

Proving the bound $\left ( 1+\frac{x}{n} \right)^n \leqslant 3^x$, $\forall x \in \mathbb{R^+}$

asked Sep 17, 2014 at 17:52

3 votes

1 answer

139 views

Show that $\int_0^r \frac{\mathrm{d}t}{\sqrt{r^2 - t^2}} $ is independent of $r$

asked Nov 3, 2014 at 11:49

3 votes

4 answers

125 views

$\lim_{n\to\infty}n^{n\cdot a_{n}}=1$ as a sufficient condition for $\sum a_{n}<\infty$

asked Aug 1, 2012 at 5:16

3 votes

2 answers

538 views

$\lim\limits_{n \to\infty}x_n-x_{n+1}=0$, $x_{n_k}$ converges but $x_n$ does not converge

asked Jun 6, 2012 at 14:32

3 votes

3 answers

2k views

Permutations with a cycle $>\frac{n}{2}$

asked Dec 15, 2012 at 16:19

3 votes

2 answers

158 views

If $L\in REG$ then $M$ has a finite number of distinct rows

asked Mar 11, 2013 at 19:23

3 votes

1 answer

4k views

Number of permutations with a single fixed point

asked Jan 21, 2012 at 18:53

3 votes

1 answer

432 views

How many solutions exist for a non-linear system

asked Nov 2, 2015 at 14:49

2 votes

1 answer

124 views

Probability a random graph has a subset of $t$ vertices with $3t$ edges

asked Mar 7, 2018 at 8:14

2 votes

1 answer

193 views

Coupon Collector problem - 2nd moment method

asked Oct 1, 2018 at 22:46

2 votes

2 answers

401 views

Prove that $\lim\limits_{x\to\infty}\frac{\ln^{\delta}(x)}{x^{\varepsilon}}=0 $ for every $\delta\in\mathbb{R}$ and $\varepsilon >0$

asked May 22, 2012 at 20:15

2 votes

1 answer

433 views

An example to divergent sequence that there exists parenthesization such that it converges upon

asked May 29, 2012 at 13:21

2 votes

0 answers

44 views

Probability for a regular matrix

asked Apr 9, 2013 at 19:04

2 votes

1 answer

110 views

How to formally justify that $\int o(x) \, dx\sim o(x^2)$?

asked Jun 8, 2012 at 11:35

2 votes

2 answers

85 views

If $\lim_{n \to \infty}2^n|a_{n+1}-a_n|=L>0$ then $a_n$ converges

asked Oct 25, 2015 at 15:03

1 vote

2 answers

3k views

Prove that if $\lim_{n \to \infty} |a_{n+1}-a_n|=0$ then $a_n$ converges

asked Oct 19, 2015 at 10:04

1 vote

1 answer

141 views

Star graph embeddings

asked Jul 5, 2013 at 10:17

1 vote

1 answer

111 views

A basic group question

asked Aug 6, 2012 at 22:58

Stack Exchange Network

47 Questions

Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?

Interesting Math for 3-graders

Construction of a right triangle

What's the name of this quantity?

dissection of a $1\times 5$ rectangle to a square

Approximating Increasing Sequence

If $\sum\limits_{k=1}^{\infty}a_k=S $, then $ a_4+a_3+a_2+a_1+a_8+a_7+a_6+a_5+\dots=?$

Evaluating $\frac{1}{\sqrt{4}+\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}+\sqrt{16}}+\frac{1}{\sqrt{16}+\sqrt{20}+\sqrt{25}}=?$

Is it a "paradox", or a flaw in the question?

Proving that $\int_0 ^1 \frac{\text{d}s}{\sqrt{1-s^2}}$ converges with no trig functions

Elementary proof for $\text{rank} \left(A \otimes B \right) = \text{rank}A\cdot \text{rank}B$

Proof for $\forall x$, $\exists y$ s.t $1/2 \le |x-y|\le 1$ and $ |\cos \pi x - \cos \pi y|\ge 1$

Proving the bound $\left ( 1+\frac{x}{n} \right)^n \leqslant 3^x$, $\forall x \in \mathbb{R^+}$

Show that $\int_0^r \frac{\mathrm{d}t}{\sqrt{r^2 - t^2}} $ is independent of $r$

$\lim_{n\to\infty}n^{n\cdot a_{n}}=1$ as a sufficient condition for $\sum a_{n}<\infty$

$\lim\limits_{n \to\infty}x_n-x_{n+1}=0$, $x_{n_k}$ converges but $x_n$ does not converge

Permutations with a cycle $>\frac{n}{2}$

If $L\in REG$ then $M$ has a finite number of distinct rows

Number of permutations with a single fixed point

How many solutions exist for a non-linear system

Probability a random graph has a subset of $t$ vertices with $3t$ edges

Coupon Collector problem - 2nd moment method

Prove that $\lim\limits_{x\to\infty}\frac{\ln^{\delta}(x)}{x^{\varepsilon}}=0 $ for every $\delta\in\mathbb{R}$ and $\varepsilon >0$

An example to divergent sequence that there exists parenthesization such that it converges upon

Probability for a regular matrix

How to formally justify that $\int o(x) \, dx\sim o(x^2)$?

If $\lim_{n \to \infty}2^n|a_{n+1}-a_n|=L>0$ then $a_n$ converges

Prove that if $\lim_{n \to \infty} |a_{n+1}-a_n|=0$ then $a_n$ converges

Star graph embeddings

A basic group question