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VIVID
  • Member for 4 years, 2 months
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17 votes
2 answers
606 views

How large is the area that the bug can access?

9 votes
2 answers
218 views

Calculate the determinant of $n^\text{th}$ order

8 votes
0 answers
145 views

Show that all terms of this sequence are integers.

7 votes
1 answer
151 views

If $\tan x + \tan y = 4$ and $\cos x + \cos y = 1/5$, find $\tan(x+y)$.

7 votes
2 answers
296 views

Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$

6 votes
2 answers
119 views

Calculate $\lim_{n\to\infty} \frac{ (1^{1^p}2^{2^p}\cdot...\cdot n^{n^p})^{ 1/n^{p+1} }}{n^{1/(p+1)}}$ [duplicate]

6 votes
2 answers
216 views

Prove that $\lim_{n\to\infty} \frac{a_n}{a_{n+1}} = p$ [duplicate]

5 votes
1 answer
337 views

Let $\lambda$ be a real eigenvalue of matrix $AB$. Prove that $|\lambda| > 1$.

5 votes
5 answers
163 views

Can one deduce that $P(x)$ is a polynomial of degree $0$ or $1$ from the following condition

4 votes
1 answer
90 views

How to show that $AB=BA$ if $(A-3I)(B-3I)=2B+9I$

4 votes
2 answers
160 views

Prove the following inequality $\sum_{i<j<k}\frac{a_ia_ja_k}{(n-2)(n-1)n}\le \bigg(\sum_{i<j}\frac{a_ia_j}{(n-1)n}\bigg)^2+\frac{1}{12}$

4 votes
2 answers
195 views

Choosing the sign of determinant when taking a square root

4 votes
2 answers
64 views

show that the set of all real $y$ 's such that $\lim_{n\rightarrow \infty}f'(x_n)=y$, is equal to the segment $[p,q]$ for some $p\not = q$

4 votes
4 answers
458 views

Find the asymptotes to the hyperbola $3x^2+2xy-y^2+8x+10y+14=0$

4 votes
1 answer
132 views

Compute $\sum_{x\in\mathcal{N}}\sum_{y\in\mathcal{N}}\frac{1}{x+y+1}$

3 votes
1 answer
232 views

Can one divide a convex polygon into two convex polygons of the same area, with parallelly moving a given straight line on a plane?

3 votes
1 answer
98 views

Find the conditions on $(a,b,c)$ so that the following integral converges

2 votes
1 answer
61 views

For any prime $p>3$ show that $C_{np}^{p}-C_{np}^{2p}+C_{np}^{3p}-C_{np}^{4p}+...+(-1)^{n-1}C_{np}^{np} \equiv 1\pmod{p^3}$

2 votes
1 answer
72 views

What is a geometric interpretation of $0x+0y=0$ [closed]

2 votes
3 answers
81 views

Find $a_{2020}$ in the sequence

2 votes
1 answer
120 views

Limit with fractional part of a rational number exists.

2 votes
1 answer
127 views

Evaluate the value of $\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$ where $x_n=x_{n-1}^2-2, x_1=5$ [duplicate]

2 votes
1 answer
50 views

Show that $v(P+v^Tv)^{-1}v^T \in (0,1)$

2 votes
2 answers
311 views

Remove some digits and re-order the digits (if necessary) so that the resulting integer would be the maximum possible integer that is divisible by 3.

2 votes
2 answers
81 views

Can we say anything about the existence of $\lim(a_n-a_{n-1})$

2 votes
1 answer
90 views

Find the number of all natural solutions to $0<\sin n < 10^{-12}, \ \ n\in \mathbb{N}$

2 votes
4 answers
748 views

Show that $f(x,y) = \sin( x )|y|$ is differentible at $(0,0)$.

2 votes
4 answers
180 views

Simplify $\frac{4\cos ^2\left(2x\right)-4\cos ^2\left(x\right)+3\sin ^2\left(x\right)}{4\sin ^2\left(x\right)-\sin ^2\left(2x\right)}$

2 votes
1 answer
80 views

Convergence of $\int_0^\infty \frac{\ln(1+x^{-2a})}{\sqrt{x^a+x^{-a}}}dx$ without Gamma function

2 votes
2 answers
77 views

If $\sum_{k=0}^2 c_kf^{(k)}(x) \ge 0$ show that $f(x)$ is a non-negative polynomial