User CuriousMind

11 votes

3 answers

508 views

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

real-analysis sequences-and-series

asked Sep 25, 2021 at 23:58

9 votes

3 answers

707 views

Prove two angles add up to 90 degrees

asked Aug 17, 2020 at 1:45

9 votes

1 answer

298 views

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

probability probability-theory probability-distributions

asked Oct 15, 2020 at 2:43

8 votes

3 answers

218 views

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

geometry contest-math euclidean-geometry

asked Dec 22, 2018 at 14:07

7 votes

1 answer

85 views

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

number-theory polynomials

asked Dec 25, 2018 at 3:45

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) $

inequality optimization contest-math symmetric-polynomials buffalo-way

asked Jun 14, 2020 at 14:10

5 votes

1 answer

268 views

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

linear-algebra matrices numerical-methods eigenvalues-eigenvectors numerical-linear-algebra

asked Aug 5, 2021 at 23:43

4 votes

2 answers

227 views

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

integration definite-integrals indefinite-integrals

asked Jul 25, 2021 at 13:39

3 votes

0 answers

87 views

Proving the matrix is positive semidefintie through integrals

linear-algebra integration matrices inequality positive-semidefinite

asked Jul 25, 2021 at 23:05

3 votes

3 answers

131 views

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

complex-analysis algebra-precalculus elementary-number-theory complex-numbers recreational-mathematics

asked Apr 12, 2020 at 1:24

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 $(0,1)$

polynomials roots recreational-mathematics

asked Aug 4, 2019 at 1:12

3 votes

1 answer

270 views

The intuition behind the definition of the definiteness of a matrix

linear-algebra matrices intuition positive-definite positive-semidefinite

asked Oct 18, 2019 at 0:14

3 votes

2 answers

114 views

$16$ people around a round table

combinatorics puzzle

asked Oct 20, 2019 at 13:25

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})$

algebra-precalculus polynomials complex-numbers

asked Dec 6, 2019 at 12:44

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 $c = c_1...c_n$

linear-algebra matrices proof-explanation determinant

asked Dec 17, 2019 at 21:55

2 votes

2 answers

340 views

Sum of Liouville's function

number-theory elementary-number-theory

asked Sep 14, 2019 at 3:37

2 votes

4 answers

239 views

Linear Algebra question on positive definite matrix

linear-algebra

asked Mar 9, 2015 at 18:54

2 votes

1 answer

406 views

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

probability

asked Apr 20, 2015 at 1:04

2 votes

2 answers

258 views

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

contest-math euclidean-geometry recreational-mathematics plane-geometry

asked Jun 26, 2020 at 21:32

2 votes

1 answer

316 views

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

linear-algebra eigenvalues-eigenvectors numerical-linear-algebra

asked Aug 7, 2021 at 1:53

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

elementary-number-theory recurrence-relations systems-of-equations

asked Jan 7 at 22:09

1 vote

2 answers

77 views

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

multivariable-calculus optimization vector-analysis matrix-calculus

asked Aug 28, 2021 at 1:49

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 $x$

linear-algebra matrices vector-analysis matrix-calculus

asked Aug 28, 2021 at 23:44

1 vote

1 answer

275 views

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

probability stochastic-processes solution-verification markov-chains expected-value

asked May 21, 2020 at 2:44

1 vote

3 answers

134 views

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

sequences-and-series summation binomial-coefficients telescopic-series

asked Feb 14, 2021 at 14:39

1 vote

1 answer

73 views

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

algebra-precalculus elementary-number-theory inequality contest-math

asked Dec 28, 2020 at 15:40

1 vote

5 answers

95 views

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

integration limits definite-integrals limits-without-lhopital

asked Dec 29, 2020 at 19:10

1 vote

2 answers

220 views

Number of binary matrices whose rows/columns are weakly monotone

combinatorics

asked Nov 29, 2018 at 19:00

1 vote

1 answer

135 views

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

algebra-precalculus inequality optimization contest-math

asked Aug 7, 2019 at 12:11

0 votes

2 answers

92 views

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

algebra-precalculus

asked Jan 17, 2020 at 1:10

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43 Questions

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

Prove two angles add up to 90 degrees

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

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

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

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) $

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

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

Proving the matrix is positive semidefintie through integrals

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

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

The intuition behind the definition of the definiteness of a matrix

$16$ people around a round table

$\omega$ 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})$

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 $c = c_1...c_n$

Sum of Liouville's function

Linear Algebra question on positive definite matrix

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

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

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

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

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

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

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

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

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

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

Number of binary matrices whose rows/columns are weakly monotone

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

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