User Analysis - Mathematics Stack Exchange

16 votes

3 answers

492 views

Bisection of a a triangular area

asked Aug 21, 2019 at 20:45

6 votes

2 answers

145 views

Showing that $1+2020^y$ ($y\in \mathbb{Z}$) is not a perfect square

asked Mar 1, 2020 at 19:08

6 votes

2 answers

141 views

Let $M\in \text{SO}(3,\mathbb{R})$, prove that $\det(M-I_3)=0$.

asked Sep 18, 2021 at 16:17

4 votes

1 answer

90 views

Showing that $\exp(rN_t-\lambda t(e^r-1))$ is a Martingale

asked Jun 27, 2023 at 19:39

4 votes

1 answer

853 views

Understanding Sturm's theorem

asked Aug 3, 2021 at 14:25

4 votes

0 answers

58 views

Proving that $f(x,y)=(2x^2-y)(y-x^2)$ has positive and negative function values in every neighborhood around $(0,0)$

asked Aug 23, 2021 at 0:59

3 votes

1 answer

132 views

How can simplex coordinates simplify this integration?

asked Dec 30, 2020 at 22:03

3 votes

0 answers

113 views

How many vectors $w\in V$ such that $v_1,...,v_d,w$ are linearly independent?

asked May 24, 2020 at 19:11

3 votes

0 answers

76 views

Filtration dependence of martingales

asked Sep 3, 2023 at 17:26

3 votes

1 answer

86 views

What's the probability of $HTHT$ occuring before $HHTT$?

asked May 29, 2023 at 15:22

3 votes

3 answers

105 views

What does $\sum_{1\le k\le n}$ mean in this context?

asked May 30, 2023 at 21:28

3 votes

3 answers

356 views

Recursion for the number of words of length $n$ over the alphabet $\{0, 1, 2\}$ such that there are neither $11$ nor $22$ blocks

asked Mar 30, 2022 at 8:43

3 votes

2 answers

122 views

Is $\mathcal{A}\vee \mathcal{B}=\{A\cup B : A\in \mathcal{A}, B\in \mathcal{B}\}$ a $\sigma$-Algebra?

asked Jun 1, 2022 at 21:51

3 votes

1 answer

98 views

How to compute $\sum_{n,m=2}^{\infty}{n^{-m}}$

asked Aug 19, 2019 at 12:54

3 votes

2 answers

121 views

Continuity with dense sets?

asked Sep 19, 2019 at 14:46

3 votes

3 answers

135 views

Proof verification: If $g\circ f$ is surjective, show that $g$ is surjective.

asked Jul 30, 2019 at 0:57

3 votes

1 answer

131 views

If $\lim\limits_{h\to 0^+}\frac{f(x+h)-f(x)}{h}=0$ for all $x\in I$, then $f$ is constant.

asked Oct 20, 2019 at 0:08

3 votes

1 answer

150 views

Show that $\sqrt[k]{a}\leq a_{n+1}\leq a_n$ for $n\in \mathbb{N}$

asked Jun 1, 2019 at 10:37

3 votes

3 answers

128 views

Is there a way to re-write $\sum_{n=1}^{\infty}{\left(\sum_{k=1}^{n}{\frac{1}{k}}\right)}z^n$

asked Jun 24, 2019 at 21:16

2 votes

3 answers

116 views

How to compute $\sum_{n=0}^{\infty}{\frac{2^n+5^n}{7^{n-2}}}$?

asked Jul 8, 2019 at 21:33

2 votes

1 answer

50 views

How to verify that $\lim\limits_{n\to\infty}\frac{(n+i^n)(1-n)}{n^2-n+1}=1$

asked Jul 10, 2019 at 11:29

2 votes

4 answers

97 views

How to show $c_n \leq c_{n+1}$? [duplicate]

asked Jul 10, 2019 at 16:37

2 votes

1 answer

72 views

If $f$ is uniformly continuous and $(z_n)_n$ a Cauchy sequence in $D\subset \mathbb{C}$, then $(f(z_n))_n$ is a Cauchy sequence.

asked Jul 7, 2019 at 12:34

2 votes

1 answer

91 views

Is $f: (0,\infty ) \to \mathbb{R}$ , $f(x):=\ln(x)+e^x$ injective?

asked Jul 13, 2019 at 14:43

2 votes

2 answers

165 views

How to compute $\sum_{k=1}^{\infty}{\frac{1}{k^2+2k}}$?

asked Jun 16, 2019 at 0:16

2 votes

3 answers

75 views

How to prove $n^{3/2} \le 2^n/n$ for all $n\geq 8$ via Induction?

asked May 24, 2019 at 17:10

2 votes

3 answers

72 views

Prove : For $k\in \mathbb{Z}: \lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

asked May 26, 2019 at 16:08

2 votes

2 answers

79 views

Why does $|f(x)| \leq x^2 \implies$ $f$ is differentiable in $0$?

asked Sep 23, 2019 at 19:50

2 votes

2 answers

944 views

Proof explanation: "Every convergent sequence is bounded"

asked Aug 4, 2019 at 2:23

2 votes

5 answers

73 views

Trying to understand sequence convergence proof visually

asked Aug 4, 2019 at 17:48

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296 Questions

Bisection of a a triangular area

Showing that $1+2020^y$ ($y\in \mathbb{Z}$) is not a perfect square

Let $M\in \text{SO}(3,\mathbb{R})$, prove that $\det(M-I_3)=0$.

Showing that $\exp(rN_t-\lambda t(e^r-1))$ is a Martingale

Understanding Sturm's theorem

Proving that $f(x,y)=(2x^2-y)(y-x^2)$ has positive and negative function values in every neighborhood around $(0,0)$

How can simplex coordinates simplify this integration?

How many vectors $w\in V$ such that $v_1,...,v_d,w$ are linearly independent?

Filtration dependence of martingales

What's the probability of $HTHT$ occuring before $HHTT$?

What does $\sum_{1\le k\le n}$ mean in this context?

Recursion for the number of words of length $n$ over the alphabet $\{0, 1, 2\}$ such that there are neither $11$ nor $22$ blocks

Is $\mathcal{A}\vee \mathcal{B}=\{A\cup B : A\in \mathcal{A}, B\in \mathcal{B}\}$ a $\sigma$-Algebra?

How to compute $\sum_{n,m=2}^{\infty}{n^{-m}}$

Continuity with dense sets?

Proof verification: If $g\circ f$ is surjective, show that $g$ is surjective.

If $\lim\limits_{h\to 0^+}\frac{f(x+h)-f(x)}{h}=0$ for all $x\in I$, then $f$ is constant.

Show that $\sqrt[k]{a}\leq a_{n+1}\leq a_n$ for $n\in \mathbb{N}$

Is there a way to re-write $\sum_{n=1}^{\infty}{\left(\sum_{k=1}^{n}{\frac{1}{k}}\right)}z^n$

How to compute $\sum_{n=0}^{\infty}{\frac{2^n+5^n}{7^{n-2}}}$?

How to verify that $\lim\limits_{n\to\infty}\frac{(n+i^n)(1-n)}{n^2-n+1}=1$

How to show $c_n \leq c_{n+1}$? [duplicate]

If $f$ is uniformly continuous and $(z_n)_n$ a Cauchy sequence in $D\subset \mathbb{C}$, then $(f(z_n))_n$ is a Cauchy sequence.

Is $f: (0,\infty ) \to \mathbb{R}$ , $f(x):=\ln(x)+e^x$ injective?

How to compute $\sum_{k=1}^{\infty}{\frac{1}{k^2+2k}}$?

How to prove $n^{3/2} \le 2^n/n$ for all $n\geq 8$ via Induction?

Prove : For $k\in \mathbb{Z}: \lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

Why does $|f(x)| \leq x^2 \implies$ $f$ is differentiable in $0$?

Proof explanation: "Every convergent sequence is bounded"

Trying to understand sequence convergence proof visually