User asd

7 votes

2 answers

2k views

In how many ways is possible to write a number as the ordered sum of $1$ and $2$

asked Nov 1, 2016 at 18:57

6 votes

2 answers

106 views

If $f$ is differentiable on $[1,2]$, then $\exists \alpha\in(1,2): f(2)-f(1) = \frac{\alpha^2}{2}f'(\alpha)$

asked Nov 2, 2016 at 22:13

6 votes

2 answers

5k views

Proof by induction: $(1+x)^n > 1 + nx+nx^2$

asked Jan 31, 2015 at 20:58

6 votes

2 answers

494 views

Help to understand this property: $\int\limits_{ka}^{kb}s\left(\frac{x}{k}\right)dx = k\int\limits_a^bs(x)dx$

asked Feb 20, 2015 at 14:10

6 votes

3 answers

2k views

Let $G$ be a group. Show that $\forall a, b, c \in G$, the elements $abc, bca, cab$ have the same order.

asked Apr 17, 2017 at 15:34

5 votes

5 answers

351 views

Calculate: $177^{20^{100500}}\pmod{60}$

asked Mar 22, 2017 at 21:45

5 votes

1 answer

922 views

Representing a nonnegative integer as the ordered sum of odd numbers

asked Nov 9, 2016 at 9:51

5 votes

5 answers

9k views

What's wrong?: Find the infinite sum $S = 1 + \frac{3}{4} + \frac{7}{16} + \frac{15}{64} + \frac{31}{256} + \ldots$

asked May 13, 2015 at 20:57

5 votes

1 answer

4k views

Prove: In a ⊿, the bisector of the right angle bisects the Altitude and Median drawn from that same vertex.

asked Jun 11, 2015 at 16:46

5 votes

3 answers

186 views

Proof: $n^p < \frac{(n+1)^{p+1}-n^{p+1}}{p+1} < (n+1)^p$

asked Feb 11, 2015 at 12:32

4 votes

2 answers

5k views

Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$

asked Feb 8, 2015 at 20:02

4 votes

2 answers

273 views

Proof: $2\sqrt{m}-2 < \sum\limits_{n=1}^m\frac{1}{\sqrt{n}}< 2\sqrt{m}-1$

asked Feb 9, 2015 at 19:35

4 votes

4 answers

965 views

What is the relationship between the Archimedean Property and Calculus?

asked Feb 16, 2015 at 14:15

4 votes

2 answers

1k views

How to derive this formula: $\int_a^bf(c-x)dx = \int_{c-b}^{c-a}f(x)dx$?

asked Feb 17, 2015 at 11:29

4 votes

1 answer

409 views

Sum of binomial coefficients from $\binom{2m+1}{0}$ to $ \binom{2m+1}{m} $

asked May 30, 2015 at 13:54

4 votes

1 answer

102 views

For every $n$, $\sum\limits_{m=0}^{\infty}\left(-\frac{1}{2}\right)^m\sum\limits_{l=0}^m\left(\frac{1}{2^{n-1}}-2\right)^{m-l} {n \choose l}=1$

asked Nov 22, 2016 at 22:32

3 votes

1 answer

68 views

Taylor series of $\frac{x-2}{\sqrt{x^2-4x+8}}$ at $x = 2$. Where is the mistake?

asked Nov 19, 2016 at 11:52

3 votes

2 answers

81 views

Is the set $C = \{( x_1, x_2, x_3, x_4) \in \mathbb{R}^4: x_1^2 + x_2^2 + x_3^2 < \ln(1+x_4^2)\}$ open or closed or neither?

asked Feb 24, 2017 at 21:42

3 votes

2 answers

234 views

Show that in $\lim_{x\to 0}\frac{x^3\sin(1/x)}{\sin^2 x}$ can't be applied L'Hopital's Rule

asked Nov 9, 2016 at 16:16

3 votes

5 answers

1k views

Find the $n$ derivative of $y= e^{2x}\sin^2 x$

asked Nov 21, 2016 at 20:17

3 votes

3 answers

481 views

Can the inequality $\sum\limits_{i=1}^n\frac{1}{\sqrt{i}} < 2\sqrt{n} - 1$ be proved without induction?

asked Feb 19, 2015 at 15:16

3 votes

1 answer

133 views

What is the significance of proving the integrability of monotonic functions?

asked Feb 13, 2015 at 18:06

3 votes

1 answer

3k views

Finding the number of primes numbers using exclusion/inclusion principle: What am I doing wrong?

asked Jun 10, 2015 at 12:55

2 votes

1 answer

146 views

Investigating the differentiability of $f(x) = |\sin x |$

asked Oct 26, 2016 at 22:17

2 votes

2 answers

110 views

Investigating the differentiability of $f(x) = |\pi x|sinx$

asked Oct 27, 2016 at 5:09

2 votes

0 answers

83 views

Alternating sum of subfactorials: Is there a closed form for this: $\displaystyle \sum_{i=0}^{m-2}(-1)^i\left[\frac{(m-i)!}{e}\right]$?

asked Jun 28, 2015 at 15:26

2 votes

2 answers

124 views

$\nabla \times \left(\frac{\mathbf{A \times r}}{r^3}\right)$, where $\mathbf{A}$ is independent of $\displaystyle\nabla \times$

asked Jul 16, 2015 at 22:01

2 votes

1 answer

594 views

Confusion in understanding a proof in Apostol's Calculus I

asked Jan 30, 2015 at 18:14

2 votes

0 answers

171 views

Is it correct to say that if $\lim\limits_{x \to a}f(x) = 0$ it is an Infinitesimal?

asked Feb 24, 2015 at 14:53

2 votes

3 answers

897 views

Prove that: $\lim\limits_{x \to +\infty}\frac{(\log x)^b}{x^a} = 0$ and $\lim\limits_{x \to +\infty}\frac{x^b}{e^{ax}} = 0$

asked Feb 25, 2015 at 14:18

Stack Exchange Network

79 Questions

In how many ways is possible to write a number as the ordered sum of $1$ and $2$

If $f$ is differentiable on $[1,2]$, then $\exists \alpha\in(1,2): f(2)-f(1) = \frac{\alpha^2}{2}f'(\alpha)$

Proof by induction: $(1+x)^n > 1 + nx+nx^2$

Help to understand this property: $\int\limits_{ka}^{kb}s\left(\frac{x}{k}\right)dx = k\int\limits_a^bs(x)dx$

Let $G$ be a group. Show that $\forall a, b, c \in G$, the elements $abc, bca, cab$ have the same order.

Calculate: $177^{20^{100500}}\pmod{60}$

Representing a nonnegative integer as the ordered sum of odd numbers

What's wrong?: Find the infinite sum $S = 1 + \frac{3}{4} + \frac{7}{16} + \frac{15}{64} + \frac{31}{256} + \ldots$

Prove: In a ⊿, the bisector of the right angle bisects the Altitude and Median drawn from that same vertex.

Proof: $n^p < \frac{(n+1)^{p+1}-n^{p+1}}{p+1} < (n+1)^p$

Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$

Proof: $2\sqrt{m}-2 < \sum\limits_{n=1}^m\frac{1}{\sqrt{n}}< 2\sqrt{m}-1$

What is the relationship between the Archimedean Property and Calculus?

How to derive this formula: $\int_a^bf(c-x)dx = \int_{c-b}^{c-a}f(x)dx$?

Sum of binomial coefficients from $\binom{2m+1}{0}$ to $ \binom{2m+1}{m} $

For every $n$, $\sum\limits_{m=0}^{\infty}\left(-\frac{1}{2}\right)^m\sum\limits_{l=0}^m\left(\frac{1}{2^{n-1}}-2\right)^{m-l} {n \choose l}=1$

Taylor series of $\frac{x-2}{\sqrt{x^2-4x+8}}$ at $x = 2$. Where is the mistake?

Is the set $C = \{( x_1, x_2, x_3, x_4) \in \mathbb{R}^4: x_1^2 + x_2^2 + x_3^2 < \ln(1+x_4^2)\}$ open or closed or neither?

Show that in $\lim_{x\to 0}\frac{x^3\sin(1/x)}{\sin^2 x}$ can't be applied L'Hopital's Rule

Find the $n$ derivative of $y= e^{2x}\sin^2 x$

Can the inequality $\sum\limits_{i=1}^n\frac{1}{\sqrt{i}} < 2\sqrt{n} - 1$ be proved without induction?

What is the significance of proving the integrability of monotonic functions?

Finding the number of primes numbers using exclusion/inclusion principle: What am I doing wrong?

Investigating the differentiability of $f(x) = |\sin x |$

Investigating the differentiability of $f(x) = |\pi x|sinx$

Alternating sum of subfactorials: Is there a closed form for this: $\displaystyle \sum_{i=0}^{m-2}(-1)^i\left[\frac{(m-i)!}{e}\right]$?

$\nabla \times \left(\frac{\mathbf{A \times r}}{r^3}\right)$, where $\mathbf{A}$ is independent of $\displaystyle\nabla \times$

Confusion in understanding a proof in Apostol's Calculus I

Is it correct to say that if $\lim\limits_{x \to a}f(x) = 0$ it is an Infinitesimal?

Prove that: $\lim\limits_{x \to +\infty}\frac{(\log x)^b}{x^a} = 0$ and $\lim\limits_{x \to +\infty}\frac{x^b}{e^{ax}} = 0$