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Q. Zhang
  • Member for 6 years, 3 months
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12 votes
Accepted

Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$

9 votes

Compute integral of general form $ \int_0^\infty \left(\frac{x}{\sinh x}\right)^n d x $

5 votes

Prove $x^x+y^y\ge x^2+y^2$ for $x,y>0$ and $x+y\le 2$.

5 votes

Prove that if A is an uncountable set and B is a countable set, then A-B must be uncountable

4 votes
Accepted

Finding trigonometric integral

4 votes
Accepted

Proving that $a_j=a_{j-1}+a_{j-2}$ cannot converge to a finite limit.

4 votes
Accepted

How to solve the nonlinear recurrence relation $a_{n+1} = \frac{1-a_n}{3+a_n}$

4 votes

$GL_{n}(\mathbb{Z})$ and $GL_{n+1}(\mathbb{Z})$ are not isomorphic

3 votes
Accepted

Product of symmetric matrices equals zero matrix

3 votes
Accepted

Find $p,q,r\in \mathbb Q$ such that $r^2-5=p^2$ and $r^2+5=q^2$

3 votes

Find the $n^{th}$ partial sum of a telescoping series

3 votes

Existence of a Subgroup of Order 4 in $(\mathbb{Z}/p\mathbb{Z})^{\times}$

3 votes
Accepted

$\lim_{n \rightarrow \infty} \sum_{n=1}^{n}\frac{a_n}{n}$ is equal to?

3 votes
Accepted

Vector products

2 votes

PS for $4u_{n+1}-u_n = 5\cdot4^{-n}$?

2 votes

If $p$ is prime, show that $p\mid a^2 \implies p\mid a$

2 votes
Accepted

Circle Geometry-How to prove $AC \perp BD$

2 votes

Computing a definite integral not using symmetry

2 votes
Accepted

Can we prove $\sum_{i=1}^m \frac{1}{t_i +1} \ge \sum_{i=1}^m \frac{1}{\lambda_i +1}$ or not?

2 votes

Proving that $S^1$ is closed in $\mathbb{R}^2$

2 votes
Accepted

Solving $\tan^{-1}\left(\frac{2x+1}{x+1}\right)+\tan^{-1}\left(\frac{2x-1}{x-1}\right)=2\tan^{-1}\left(1+x\right)$

2 votes
Accepted

Prove $GL(m,\Bbb{C}) \subset GL_+(2m,\Bbb{R})$

2 votes

Exercise 6, Section 3.2 of Hoffman’s Linear Algebra

2 votes

Evaluation of $\int^{\frac{\pi}{2}}_{0}\frac{\cos^6 x}{\sin x+\cos x}dx$

2 votes

Prove $2 < 1/a + 1/b < \mathrm{e}$ provided $b\ln a - a\ln b = a - b$

1 vote

$\text{rank}(I+AB) = \text{rank}(I+BA)$

1 vote
Accepted

Does it always hold that $n-\operatorname{rank}(A)=\operatorname{rank}(I_n-BA)-\operatorname{rank}(A(I_n-BA))$

1 vote
Accepted

If the characteristic function of $A$ is $(\lambda - 1)^n$ then $A^k$ is similar to $A$

1 vote

Suppose a sequence ${x_n}$ converges. Prove that $\displaystyle\lim_{n\rightarrow\infty} \sqrt{|x_n|} = \sqrt{|\lim_{n\rightarrow\infty} x_n|}$

1 vote

Does $k[M]\cong k^m$ mean $M$ is diagonalizable?