User actinidia

9 votes

1 answer

688 views

How did Euler disprove Mersenne's conjecture?

asked Dec 18, 2017 at 14:53

7 votes

8 answers

297 views

Showing that $ 1 + 2 x + 3 x^2 + 4 x^3 + \cdots + x^{10} = (1 + x + x^2 + x^3 + x^4 + x^5)^2$

asked Feb 9, 2018 at 18:17

5 votes

1 answer

150 views

Does having closed forms of two generating functions guarantee that one can find the closed form of their term-by-term product?

asked Feb 5, 2018 at 19:03

4 votes

2 answers

98 views

Jumping-index summations

asked Dec 19, 2017 at 16:27

4 votes

6 answers

3k views

Alternating dice roll game

asked Nov 9, 2017 at 1:41

4 votes

2 answers

172 views

How does this numerical method of root approximation work?

asked Nov 16, 2017 at 5:22

4 votes

1 answer

111 views

Analytically finding the value of $n$ for which $n \prod\limits_{k=0}^{n-1}\frac{60-k}{60}$ is maximized

asked Mar 6, 2018 at 21:35

4 votes

0 answers

125 views

Improving clarity and argumentation with hard-to-describe combinatorial proof

asked Apr 18, 2018 at 16:56

4 votes

4 answers

127 views

Showing differentiability of $g(x)=\begin{cases}\frac{f(x)}{x},&\text{$x\neq0$}\\f'(0),&x=0\end{cases}$ given that $f(0)=0$

asked Nov 14, 2018 at 9:29

3 votes

1 answer

343 views

In Baby Rudin's Theorem 1.1, why is it important that $S$ has the least upper bound property?

asked Sep 8, 2018 at 23:23

3 votes

3 answers

757 views

Why is $\text{Li}(x)$ a much better estimate of $\pi(x)$ than $\frac{x}{\log x}$?

asked Nov 10, 2017 at 16:11

2 votes

2 answers

763 views

Can definite integrals be indeterminate?

asked Dec 9, 2017 at 19:09

2 votes

1 answer

134 views

Ordinary generating function for $\mu^2(x)$

asked May 2, 2018 at 21:31

2 votes

1 answer

853 views

$f:[0,1] \times [0,1] → \mathbb R$ is continuous. Prove that $g(x) = \max\{f(x,y) : y \in [0,1]\}$ is defined and continuous.

asked Nov 14, 2018 at 10:57

2 votes

1 answer

48 views

Is Nim a (strong) positional game?

asked Jan 30, 2019 at 10:41

2 votes

4 answers

191 views

Intuition behind the fact that $X,Y$ i.i.d $\not \implies \mathbb E[X|A] = \mathbb E[Y]$

asked Mar 22, 2019 at 4:03

2 votes

2 answers

160 views

The series $\sum_n^\infty a_n^p$ where $\{a_n\}_{n=1}^\infty$ is a convergent, strictly positive sequence

asked Oct 18, 2018 at 12:10

2 votes

1 answer

840 views

Recovering a pdf from quantile function

asked Aug 23, 2020 at 4:51

2 votes

1 answer

65 views

What kind of ODE is this, and what method do I use to solve it?

asked Sep 25, 2020 at 15:52

1 vote

1 answer

59 views

What distribution looks like a uniform distribution with decaying density at the extremes?

asked Aug 18, 2020 at 4:48

1 vote

1 answer

20 views

Are the multiplications in $\langle v | \bar U^{\operatorname{T}} U | v \rangle$ commutative?

asked Sep 23, 2020 at 5:52

1 vote

1 answer

473 views

Reasoning/intuition behind manipulation of variances

asked Dec 14, 2017 at 13:45

1 vote

3 answers

976 views

Differentiating the trace of $X^T A X$

asked Nov 14, 2019 at 3:28

1 vote

1 answer

63 views

Understanding proof about uniform permutations

asked Feb 26, 2020 at 2:34

1 vote

1 answer

37 views

Inductive proof of the number of ways to color $n$ identical balls with $j$ colors

asked Mar 3, 2020 at 22:47

1 vote

1 answer

48 views

Are there methods for "recovering" a sequence $a_n$ if we are given that $\sum_{k=0}^{f(x)} a_k = x$ for all $x$?

asked May 6, 2020 at 4:39

1 vote

1 answer

50 views

How does one apply "risk tolerance" to a random walk?

asked Jun 29, 2018 at 18:07

1 vote

1 answer

45 views

Distributing boys and girls in seats with relational restrictions

asked Feb 22, 2018 at 18:37

1 vote

0 answers

102 views

Proof of McMahon's factorisatio numerorum result

asked Apr 19, 2018 at 18:07

1 vote

1 answer

184 views

Simplifying a sum involving Stirling numbers of the second kind

asked Apr 25, 2018 at 9:28

Stack Exchange Network

64 Questions

How did Euler disprove Mersenne's conjecture?

Showing that $ 1 + 2 x + 3 x^2 + 4 x^3 + \cdots + x^{10} = (1 + x + x^2 + x^3 + x^4 + x^5)^2$

Does having closed forms of two generating functions guarantee that one can find the closed form of their term-by-term product?

Jumping-index summations

Alternating dice roll game

How does this numerical method of root approximation work?

Analytically finding the value of $n$ for which $n \prod\limits_{k=0}^{n-1}\frac{60-k}{60}$ is maximized

Improving clarity and argumentation with hard-to-describe combinatorial proof

Showing differentiability of $g(x)=\begin{cases}\frac{f(x)}{x},&\text{$x\neq0$}\\f'(0),&x=0\end{cases}$ given that $f(0)=0$

In Baby Rudin's Theorem 1.1, why is it important that $S$ has the least upper bound property?

Why is $\text{Li}(x)$ a much better estimate of $\pi(x)$ than $\frac{x}{\log x}$?

Can definite integrals be indeterminate?

Ordinary generating function for $\mu^2(x)$

$f:[0,1] \times [0,1] → \mathbb R$ is continuous. Prove that $g(x) = \max\{f(x,y) : y \in [0,1]\}$ is defined and continuous.

Is Nim a (strong) positional game?

Intuition behind the fact that $X,Y$ i.i.d $\not \implies \mathbb E[X|A] = \mathbb E[Y]$

The series $\sum_n^\infty a_n^p$ where $\{a_n\}_{n=1}^\infty$ is a convergent, strictly positive sequence

Recovering a pdf from quantile function

What kind of ODE is this, and what method do I use to solve it?

What distribution looks like a uniform distribution with decaying density at the extremes?

Are the multiplications in $\langle v | \bar U^{\operatorname{T}} U | v \rangle$ commutative?

Reasoning/intuition behind manipulation of variances

Differentiating the trace of $X^T A X$

Understanding proof about uniform permutations

Inductive proof of the number of ways to color $n$ identical balls with $j$ colors

Are there methods for "recovering" a sequence $a_n$ if we are given that $\sum_{k=0}^{f(x)} a_k = x$ for all $x$?

How does one apply "risk tolerance" to a random walk?

Distributing boys and girls in seats with relational restrictions

Proof of McMahon's factorisatio numerorum result

Simplifying a sum involving Stirling numbers of the second kind