User Alec

62 votes

17 answers

9k views

Which is larger? $20!$ or $2^{40}$?

asked Nov 11, 2013 at 15:08

8 votes

5 answers

439 views

Evaluating $\int\limits_0^\infty \frac{e^x}{1+e^{2x}}\mathrm dx$, alternate methods

calculus definite-integrals improper-integrals

asked Apr 9, 2015 at 7:20

8 votes

2 answers

2k views

If a function is continuous everywhere, but undefined at one point, is it still continuous?

limits continuity piecewise-continuity

asked Nov 20, 2018 at 9:58

7 votes

2 answers

136 views

Integrating $\frac{1}{(1-x)^2} $ into two different-looking functions

calculus integration derivatives indefinite-integrals

asked Dec 4, 2020 at 15:11

6 votes

4 answers

417 views

Optimal route consisting of rowing then walking

trigonometry derivatives optimization

asked Oct 3, 2017 at 20:50

6 votes

5 answers

550 views

Calculating $\sum\limits_{n=1}^{\infty}\frac{(-1)^n \sin(n)}{n}$

sequences-and-series infinity

asked Dec 21, 2017 at 22:20

5 votes

2 answers

2k views

Why is the implication "If pigs could fly, I'd be king" a true implication? [duplicate]

logic propositional-calculus

asked May 25, 2015 at 18:22

5 votes

2 answers

207 views

Last digit of $235!^{69}$

modular-arithmetic exponentiation factorial

asked Feb 6, 2016 at 18:32

5 votes

2 answers

2k views

Making a piecewise function continuous and differentiable at point

calculus functions derivatives

asked Oct 21, 2014 at 9:33

4 votes

1 answer

325 views

Showing that any group of order 286331153 is abelian

abelian-groups

asked May 15, 2014 at 15:14

4 votes

0 answers

217 views

Geometry puzzle - Show that $x = y$ [closed]

geometry puzzle

asked Nov 28, 2015 at 14:08

4 votes

2 answers

1k views

How to determine if an equation is algebraically solvable?

algebra-precalculus numerical-methods

asked Dec 7, 2015 at 18:10

4 votes

4 answers

2k views

Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$

calculus sequences-and-series taylor-expansion

asked Feb 17, 2015 at 19:40

4 votes

1 answer

153 views

Proving continuity for $2x+1$ at $x=2$ using epsilon/delta

real-analysis continuity epsilon-delta

asked Sep 16, 2016 at 20:48

3 votes

2 answers

518 views

For a primitive pythagorean triple $(a, b, c)$, prove $(c+b), (c-b)$ are both squares.

elementary-number-theory prime-factorization square-numbers pythagorean-triples

asked Jan 3, 2018 at 4:37

3 votes

4 answers

123 views

$25! \pmod {78125}$

elementary-number-theory modular-arithmetic factorial congruences

asked Dec 17, 2017 at 22:37

3 votes

1 answer

51 views

Partitions of $\mathbb Z$

elementary-set-theory

asked Jun 27, 2017 at 6:59

3 votes

1 answer

195 views

Integral test to show that $\sum_{n=2}^{\infty}\frac1{n(\ln(n))^p}$ converges for $p>1$ and diverges otherwise.

sequences-and-series definite-integrals improper-integrals

asked Feb 15, 2017 at 20:05

3 votes

3 answers

127 views

Not defining the imaginary number $i$ as the principal square root of $-1$.

complex-numbers definition

asked May 21, 2019 at 10:20

3 votes

5 answers

257 views

Determine con-/divergence of $\sum\limits_{n=1}^{\infty}\frac{1+2+\cdots+n}{2^n}$

calculus sequences-and-series

asked Feb 26, 2015 at 20:55

3 votes

3 answers

151 views

How many of the numbers in $A=\{1!,2!,...,2015!\}$ are square numbers?

contest-math factorial square-numbers

asked Jul 17, 2015 at 11:31

3 votes

1 answer

137 views

Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$

induction

asked Jun 11, 2014 at 21:37

3 votes

1 answer

2k views

Mathematical XOR

logic binary decimal-expansion

asked Oct 26, 2014 at 1:50

3 votes

2 answers

3k views

Finding equation for conic section given five points

conic-sections

asked Jan 10, 2015 at 1:37

3 votes

4 answers

62 views

Given $\vec r(t)$, what are $\vec v(t), \ v(t), \ \vec a(t), \ a(t)$?

conic-sections parametric

asked Jan 20, 2015 at 7:03

2 votes

1 answer

165 views

Determining conic section equation given foci and sum of distance to each point

conic-sections

asked Jan 18, 2015 at 19:37

2 votes

2 answers

1k views

How does the eccentricity of a conic section define its shape?

conic-sections

asked Jan 14, 2015 at 8:35

2 votes

1 answer

3k views

Parameterizing an ellipse

parametric

asked Nov 13, 2014 at 9:17

2 votes

4 answers

6k views

Proving by calculation that $\arg(-2) = \pi$

complex-numbers

asked Jun 18, 2014 at 1:57

2 votes

1 answer

71 views

Existence of limit when encountering $\frac00$

limits

asked Jun 21, 2014 at 5:42

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146 Questions

Which is larger? $20!$ or $2^{40}$?

Evaluating $\int\limits_0^\infty \frac{e^x}{1+e^{2x}}\mathrm dx$, alternate methods

If a function is continuous everywhere, but undefined at one point, is it still continuous?

Integrating $\frac{1}{(1-x)^2} $ into two different-looking functions

Optimal route consisting of rowing then walking

Calculating $\sum\limits_{n=1}^{\infty}\frac{(-1)^n \sin(n)}{n}$

Why is the implication "If pigs could fly, I'd be king" a true implication? [duplicate]

Last digit of $235!^{69}$

Making a piecewise function continuous and differentiable at point

Showing that any group of order 286331153 is abelian

Geometry puzzle - Show that $x = y$ [closed]

How to determine if an equation is algebraically solvable?

Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$

Proving continuity for $2x+1$ at $x=2$ using epsilon/delta

For a primitive pythagorean triple $(a, b, c)$, prove $(c+b), (c-b)$ are both squares.

$25! \pmod {78125}$

Partitions of $\mathbb Z$

Integral test to show that $\sum_{n=2}^{\infty}\frac1{n(\ln(n))^p}$ converges for $p>1$ and diverges otherwise.

Not defining the imaginary number $i$ as the principal square root of $-1$.

Determine con-/divergence of $\sum\limits_{n=1}^{\infty}\frac{1+2+\cdots+n}{2^n}$

How many of the numbers in $A=\{1!,2!,...,2015!\}$ are square numbers?

Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$

Mathematical XOR

Finding equation for conic section given five points

Given $\vec r(t)$, what are $\vec v(t), \ v(t), \ \vec a(t), \ a(t)$?

Determining conic section equation given foci and sum of distance to each point

How does the eccentricity of a conic section define its shape?

Parameterizing an ellipse

Proving by calculation that $\arg(-2) = \pi$

Existence of limit when encountering $\frac00$