User Robert D-B

12 votes

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?

answered Dec 7, 2017 at 15:18

11 votes

Are there primes arbitrarily close to powers?

answered Nov 23, 2019 at 1:23

6 votes

Accepted

Is every submodule of cyclic module over PID cyclic?

answered Jul 6, 2020 at 23:21

5 votes

Exponential generating function of the falling factorial

answered Nov 25, 2019 at 0:29

5 votes

Accepted

Dummit and Foote problem 11 in section 7.4

answered Aug 16, 2018 at 4:02

5 votes

Find the sum $\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{41+\cdots}}}}}$

answered Jan 20, 2019 at 5:05

4 votes

Simplify [p∧ (¬(¬p v q)) ] v (p ∧ q) so that it become p, q, ¬p, or ¬q

answered Feb 15, 2019 at 23:03

3 votes

Accepted

If a finite group $G$ acts transitively on a set of order $p^m$, then so does any $p$-Sylow subgroup

answered Jun 23, 2020 at 21:32

3 votes

Why does $11! - 10!$ equal $10!$ plus an extra digit in "ones"?

answered Aug 11, 2018 at 4:46

3 votes

Accepted

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

answered May 3, 2018 at 4:25

3 votes

Does this combinatorial identity hold？

answered Jun 5 at 21:31

2 votes

Perrin sequence and prime numbers

answered Apr 10 at 19:29

2 votes

Accepted

Can you tile a heart with dominoes?

answered Mar 6, 2021 at 18:49

2 votes

Closed form for $T_n$ if $T_{n+3}=2 T_{n+2}+2 T_{n+1}-T_{n}$

answered Mar 9, 2022 at 5:20

2 votes

Accepted

$ {a_n}^{1/k} \rightarrow m^{1/k}$

answered Aug 12, 2015 at 17:12

2 votes

Generating function $3^n + 7^n$ for $n \in \mathbb{N}_0$

answered Feb 7, 2019 at 23:08

2 votes

Probability at specific point in normal distribution curve

answered Feb 9, 2019 at 16:00

2 votes

Why is it wrong to start the inductive step with p(k)?

answered Jul 3, 2020 at 23:39

2 votes

Accepted

A summation identity

answered Jun 22, 2020 at 15:58

2 votes

Calculating value of series by taking the difference

answered Aug 7, 2019 at 0:27

2 votes

Accepted

Alternate Proofs that $\inf A = - \sup\left(-A\right)$ from Rudin

answered Sep 2, 2018 at 22:32

1 vote

Accepted

How someone got the idea for the completeness axiom?

answered Feb 10, 2019 at 18:32

1 vote

Accepted

Show that $\frac{d^2y}{dx^2}=-\frac{d^2x}{dy^2} / \left(\frac{dx}{dy}\right)^3$ is an identity

answered Jan 1, 2016 at 21:26

1 vote

Supremum and infimum definition

answered Aug 18, 2018 at 14:31

1 vote

What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?

answered Apr 16, 2018 at 14:03

1 vote

Accepted

Is it possible to use Lagrange multiplier to solve this problem?

answered May 5, 2018 at 18:59

1 vote

Sum of a particular arithmetic sequence

answered May 5, 2018 at 19:56

1 vote

What books are there to read demonstrations?

answered May 10, 2018 at 22:43

1 vote

Accepted

Why isn't $F_{X}^{-1}(U) \sim F_{X}(x) $?

answered May 10, 2018 at 19:01

1 vote

Suppose $a,b,c,$ and $d$ are real numbers, $0 \lt a \lt b $, and $d \gt 0$. Prove that if $ac \ge bd$ then $c \gt d$

answered May 11, 2018 at 4:19

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46 Answers

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?

Are there primes arbitrarily close to powers?

Is every submodule of cyclic module over PID cyclic?

Exponential generating function of the falling factorial

Dummit and Foote problem 11 in section 7.4

Find the sum $\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{41+\cdots}}}}}$

Simplify [p∧ (¬(¬p v q)) ] v (p ∧ q) so that it become p, q, ¬p, or ¬q

If a finite group $G$ acts transitively on a set of order $p^m$, then so does any $p$-Sylow subgroup

Why does $11! - 10!$ equal $10!$ plus an extra digit in "ones"?

Rings in which the "mistake" $(x + y) / d = x / d + y$ is justified

Does this combinatorial identity hold？

Perrin sequence and prime numbers

Can you tile a heart with dominoes?

Closed form for $T_n$ if $T_{n+3}=2 T_{n+2}+2 T_{n+1}-T_{n}$

$ {a_n}^{1/k} \rightarrow m^{1/k}$

Generating function $3^n + 7^n$ for $n \in \mathbb{N}_0$

Probability at specific point in normal distribution curve

Why is it wrong to start the inductive step with p(k)?

A summation identity

Calculating value of series by taking the difference

Alternate Proofs that $\inf A = - \sup\left(-A\right)$ from Rudin

How someone got the idea for the completeness axiom?

Show that $\frac{d^2y}{dx^2}=-\frac{d^2x}{dy^2} / \left(\frac{dx}{dy}\right)^3$ is an identity

Supremum and infimum definition

What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?

Is it possible to use Lagrange multiplier to solve this problem?

Sum of a particular arithmetic sequence

What books are there to read demonstrations?

Why isn't $F_{X}^{-1}(U) \sim F_{X}(x) $?

Suppose $a,b,c,$ and $d$ are real numbers, $0 \lt a \lt b $, and $d \gt 0$. Prove that if $ac \ge bd$ then $c \gt d$