User Richard

14 votes

3 answers

4k views

Guessing a number between $1$ and $100$ with 10 distinct questions and 9 honest answers

asked Dec 30, 2017 at 10:01

4 votes

2 answers

283 views

How does one prove $(1+x/n)^n\to e^x$ pointwise through series expansion?

asked Dec 12, 2017 at 8:54

4 votes

1 answer

77 views

If $A$ is a domain but not a field, then $(x)$ is not a maximal ideal of $A[x]$?

asked Jul 11, 2017 at 16:35

4 votes

1 answer

111 views

Does Little Fermat imply that if $p$ is prime then $x^p=x $ in $\Bbb Z/p\Bbb Z [x] $?

asked Jul 18, 2017 at 19:14

4 votes

3 answers

138 views

What is the parametric form of the unique line which crosses these other three lines?

asked Apr 27, 2018 at 11:27

4 votes

1 answer

143 views

How to prove that if $a_n=o(n) $ then $\sum_{k=0}^n\frac{a_n^k}{k!}\sim e^{a_n} $

asked Aug 31, 2018 at 15:10

2 votes

1 answer

91 views

Can $\{n!\log n\}$ converge to $1$?

asked Jul 1, 2018 at 14:13

2 votes

2 answers

258 views

Is it true that if $\lim_{n\to\infty} n^\alpha a_n=+\infty$ for some $0<\alpha<1$ then $n(1-a_n/a_{n+1})\ge-\alpha$?

asked Apr 22, 2018 at 22:07

2 votes

1 answer

52 views

With $\Delta=\{(x,\cdots,x)\}$, the set $\{f:X^n\to X^n| \ f\ \text{bijective and}\ f(\Delta)=\Delta\}$ is infinite for all $n\ge1$ if $X$ is infinite

asked Jun 17, 2018 at 23:22

2 votes

2 answers

100 views

Finding the inverse of $x^3+x^2+1$ in $\Bbb F_2[x]/(x^4+x^2)$ with the Euclidean algorithm

asked Jun 19, 2018 at 1:35

2 votes

1 answer

45 views

Why is $c=f(c)$ the infimum of $Y=\{x\in X| a\le x\le b, x\le f(x)\}$?

asked Jul 26, 2017 at 15:22

2 votes

2 answers

89 views

Solving $\lvert z \rvert z^2 = \sqrt{2}(1-i)\overline{z}$

asked Apr 14, 2016 at 17:27

2 votes

2 answers

183 views

Probability that at least two equal numbers are extracted

asked Apr 7, 2017 at 21:39

2 votes

1 answer

1k views

One-sided limits of $f'(x)$ at a point vs. one-sided limits of the difference quotient at that point

asked Apr 20, 2017 at 10:05

2 votes

1 answer

72 views

Proving $\sum \frac{a_n}{n+x}$ converges uniformly on $[0,+\infty)$

asked Dec 12, 2017 at 20:18

2 votes

1 answer

2k views

Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$

asked Jan 17, 2018 at 12:44

1 vote

1 answer

55 views

What is the probability of pulling out at least 2 hearts consecutively, having 3 extractions with replacement out of a complete deck?

asked Jan 23, 2018 at 17:11

1 vote

2 answers

73 views

For what $k$ is $g_k\circ f_k$ invertible?

asked Jan 14, 2018 at 17:25

1 vote

4 answers

101 views

Is it true that $\sum_k a_k(n)\to0$ as $n\to\infty$ if $a_k(n)\to0$ for all $k$ and $\sum_k a_k(n)$ converges for all $n$?

asked Dec 15, 2017 at 21:07

1 vote

3 answers

1k views

Is $A=\Bbb Z[i] /(3+i)$ finite?

asked Jul 15, 2017 at 3:30

1 vote

1 answer

103 views

The order of growth of $F(x)=\int_0^x f(t)dt$ if $f$ is uniformly continuous

asked Nov 20, 2017 at 20:45

1 vote

1 answer

102 views

If a series converges uniformly on $[a+\varepsilon,b) $ for all $\varepsilon>0$ and pointwise on $[a,b)$, is then the convergence uniform on $[a,b) $?

asked Dec 7, 2017 at 11:49

1 vote

3 answers

56 views

What is the length of this segment given the radius?

asked Dec 10, 2017 at 0:51

1 vote

1 answer

65 views

Finding $\lim_{x\to+\infty} \int_x^{x+x^a}\frac{dt}{\sqrt t \log t} $

asked Nov 9, 2017 at 21:43

1 vote

1 answer

158 views

When is the derivative of a quadratic spline a spline itself?

asked Nov 15, 2017 at 15:55

1 vote

1 answer

72 views

Showing that $f_n(x)=\left(x^n+e^{-nx}\right)^{1/n}$ converges uniformly to $f(x)=\max(x,e^{-x})$

asked Nov 17, 2017 at 10:38

1 vote

1 answer

59 views

About $A=\bigcup_{n=1}^\infty A_n$, with $A_n=\{(x,y)\in\mathbb{R^2}:-e^{-x^2/n}<y\le e^{-x^2/n}\}$

asked Apr 15, 2016 at 21:31

1 vote

3 answers

63 views

Showing that $A\cup B$ is an element of $S$

asked May 27, 2016 at 11:01

1 vote

3 answers

97 views

With $m\in\mathbb{Z^+}$ fixed, is $\sum_{m\ne n\ge1} (n^2-m^2)^{-1}$ evaluable really elementarily?

asked Jun 10, 2016 at 17:58

1 vote

2 answers

81 views

How can I solve $\frac {dy}{dx}=2\frac yx -1$?

asked Apr 28, 2017 at 18:18

Stack Exchange Network

51 Questions

Guessing a number between $1$ and $100$ with 10 distinct questions and 9 honest answers

How does one prove $(1+x/n)^n\to e^x$ pointwise through series expansion?

If $A$ is a domain but not a field, then $(x)$ is not a maximal ideal of $A[x]$?

Does Little Fermat imply that if $p$ is prime then $x^p=x $ in $\Bbb Z/p\Bbb Z [x] $?

What is the parametric form of the unique line which crosses these other three lines?

How to prove that if $a_n=o(n) $ then $\sum_{k=0}^n\frac{a_n^k}{k!}\sim e^{a_n} $

Can $\{n!\log n\}$ converge to $1$?

Is it true that if $\lim_{n\to\infty} n^\alpha a_n=+\infty$ for some $0<\alpha<1$ then $n(1-a_n/a_{n+1})\ge-\alpha$?

With $\Delta=\{(x,\cdots,x)\}$, the set $\{f:X^n\to X^n| \ f\ \text{bijective and}\ f(\Delta)=\Delta\}$ is infinite for all $n\ge1$ if $X$ is infinite

Finding the inverse of $x^3+x^2+1$ in $\Bbb F_2[x]/(x^4+x^2)$ with the Euclidean algorithm

Why is $c=f(c)$ the infimum of $Y=\{x\in X| a\le x\le b, x\le f(x)\}$?

Solving $\lvert z \rvert z^2 = \sqrt{2}(1-i)\overline{z}$

Probability that at least two equal numbers are extracted

One-sided limits of $f'(x)$ at a point vs. one-sided limits of the difference quotient at that point

Proving $\sum \frac{a_n}{n+x}$ converges uniformly on $[0,+\infty)$

Showing that the Jacobi method doesn't converge with $A=\begin{bmatrix}2 & \pm2\sqrt2 & 0 \\ \pm2\sqrt2&8&\pm2\sqrt2 \\ 0&\pm2\sqrt2&2 \end{bmatrix}$

What is the probability of pulling out at least 2 hearts consecutively, having 3 extractions with replacement out of a complete deck?

For what $k$ is $g_k\circ f_k$ invertible?

Is it true that $\sum_k a_k(n)\to0$ as $n\to\infty$ if $a_k(n)\to0$ for all $k$ and $\sum_k a_k(n)$ converges for all $n$?

Is $A=\Bbb Z[i] /(3+i)$ finite?

The order of growth of $F(x)=\int_0^x f(t)dt$ if $f$ is uniformly continuous

If a series converges uniformly on $[a+\varepsilon,b) $ for all $\varepsilon>0$ and pointwise on $[a,b)$, is then the convergence uniform on $[a,b) $?

What is the length of this segment given the radius?

Finding $\lim_{x\to+\infty} \int_x^{x+x^a}\frac{dt}{\sqrt t \log t} $

When is the derivative of a quadratic spline a spline itself?

Showing that $f_n(x)=\left(x^n+e^{-nx}\right)^{1/n}$ converges uniformly to $f(x)=\max(x,e^{-x})$

About $A=\bigcup_{n=1}^\infty A_n$, with $A_n=\{(x,y)\in\mathbb{R^2}:-e^{-x^2/n}<y\le e^{-x^2/n}\}$

Showing that $A\cup B$ is an element of $S$

With $m\in\mathbb{Z^+}$ fixed, is $\sum_{m\ne n\ge1} (n^2-m^2)^{-1}$ evaluable really elementarily?

How can I solve $\frac {dy}{dx}=2\frac yx -1$?