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CuriousMind
  • Member for 7 years, 5 months
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11 votes
3 answers
508 views

Prove that $2-\cfrac{\pi^2}{6-\cfrac{\pi^2}{10-\cfrac{\pi^2}{14-\cfrac{\pi^2}{...}}}} = 0$

9 votes
3 answers
707 views

Prove two angles add up to 90 degrees

9 votes
1 answer
298 views

$N$ kids with $k$ balls. Reshuffle. Find distribution of number of balls brought back by same kids when $N \rightarrow \infty$

8 votes
3 answers
218 views

simple looking but hard to prove geometrical problem: prove that 4 points on the same circle.

7 votes
1 answer
85 views

n-th order polynomial with all roots where all coefficients are 1 or -1, highest order of n?

7 votes
2 answers
170 views

Find maximum $k \in \mathbb{R}^{+}$ such that $ \frac{a^3}{(b-c)^2} + \frac{b^3}{(c-a)^2} + \frac{c^3}{(a-b)^2} \geq k (a+b+c) $

5 votes
1 answer
268 views

Why do we usually not need to find the eigenvalues of non-symmetric matrix

4 votes
2 answers
227 views

Prove that $\int_0^{\infty} \frac{1-\cos(at)}{t^{1+\alpha}} dt = \frac{\pi}{2 \Gamma(\alpha+1) \sin (\alpha \pi /2 )} |a|^{\alpha}$

3 votes
0 answers
87 views

Proving the matrix is positive semidefintie through integrals

3 votes
3 answers
131 views

simplify $\sqrt[3]{x \sqrt[3]{ x \sqrt[3]{x ...}} }$ -- if $x$ is negative?

3 votes
1 answer
458 views

How do I prove that $x^n+x^{n-1}+...+x^2-nx+1=0$ ($n>2$) has one and only one root in $(0,1)$

3 votes
1 answer
270 views

The intuition behind the definition of the definiteness of a matrix

3 votes
2 answers
114 views

$16$ people around a round table

3 votes
2 answers
136 views

$\omega$ satisfies $a \omega^3 + b \omega^2 + c \omega + d = 0$, Prove that $ |\omega| \leq \max( \frac{b}{a}, \frac{c}{b}, \frac{d}{c})$

2 votes
1 answer
102 views

Let $a_{i,i+1} = c_i$ for $i=1,...n$, Prove that the determinant of $I + A + A^2 + ... + A^n = (1-c)^{n-1}$ where $c = c_1...c_n$

2 votes
2 answers
340 views

Sum of Liouville's function

2 votes
4 answers
239 views

Linear Algebra question on positive definite matrix

2 votes
1 answer
406 views

Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others

2 votes
2 answers
258 views

Geometry question: Find the area of blue-shared area inside this isosceles

2 votes
1 answer
316 views

Does Rayleigh quotient iteration always find the largest eigenvalue in magnitude? If not, what are the applications?

2 votes
1 answer
142 views

Find $x_1 + x_2 + \dots+ x_{n}$ and $1^{n+1}x_1 + 2^{n+1}x_2 + \dots + {n}^{n+1}x_{n}$ given a set of linear constraints

1 vote
2 answers
77 views

matrix calculus: derivative of $\frac{x^T r}{\sqrt{x^T Sx}}$ with respect to $x$

1 vote
2 answers
76 views

$x,y$ are vectors and $\Lambda$ is a symmetric square matrix, $y = \frac{x}{\sqrt{x^T \Lambda x}}$ solve for vector $x$

1 vote
1 answer
275 views

Question on dice rolling -- expected number of rolls to get a particular sequence

1 vote
3 answers
134 views

How to compute $1 \times 2 \times 3 \times 4 + 3 \times 4 \times 5 \times 6 + ... + 97 \times 98 \times 99 \times 100$

1 vote
1 answer
73 views

Maximum of $\prod_{k=1}^{n} { f(c_k) }$ where $f(m) = \sum_{k=1}^{m} k^2, \sum_{i=1}^{n} c_i = 2020$.

1 vote
5 answers
95 views

Find $\lim_{t \rightarrow 0} \int_{0}^{t} \frac{\sqrt{1+\sin(x^2)}}{\sin t} dx$

1 vote
2 answers
220 views

Number of binary matrices whose rows/columns are weakly monotone

1 vote
1 answer
135 views

Max of $(a-x^2)(b-y^2)(c-z^2)$ when $x+y+z=a+b+c=1$, $x,y,z,a,b,c \geq 0$

0 votes
2 answers
92 views

rational roots for $5x^7+3x^2-4 =0$