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9 votes

0 answers

226 views

Generalized series for $\pi$ - What is the polynomial?

asked Sep 1, 2019 at 18:04

5 votes

4 answers

173 views

Prove that $\sum_{i=1}^{n}\frac{1}{\left(n+i\right)^{2}}\sim\frac1{2n}$

asked Nov 21, 2019 at 19:48

4 votes

4 answers

215 views

Prove $4\sin^{2}\frac{\pi}{9}-2\sqrt{3}\sin\frac{\pi}{9}+1=\frac{1}{4}\sec^{2}\frac{\pi}{9}$.

asked Feb 8, 2020 at 23:43

3 votes

1 answer

205 views

Prove that the ratio of acute angles in a $3:4:5$ triangle is irrational

asked Dec 1, 2019 at 22:55

3 votes

1 answer

476 views

Can a function be well-defined on an integral of $\mathbb{R}$ but not Lebesgue integrable?

asked Apr 6, 2018 at 14:38

3 votes

0 answers

157 views

How did the Babylonians derive the Secant Method without algebra?

asked Sep 3, 2016 at 17:56

3 votes

2 answers

151 views

Simple definition for random polynomial $p:[0,1]\to[0,1]$

asked Sep 12, 2016 at 16:17

1 vote

3 answers

151 views

Is there any well defined $f:\mathbb{R}\to\mathbb{R}$, that is not the limit of any sequence of polynomials?

asked Oct 8, 2016 at 15:25

1 vote

1 answer

50 views

If $x^a<\ln(x)<x^b$, then how are $a$ and $b$ bounded?

asked Apr 26, 2018 at 15:01

1 vote

1 answer

57 views

Does $f_0=x,f_{n+1}(x)=e^{1/f_n(x)}$ converge to $1/W(1)$?

asked Aug 28, 2018 at 11:28

1 vote

0 answers

251 views

Can a power series with no constant equal a constant?

asked Nov 12, 2019 at 21:01

0 votes

1 answer

83 views

Is $y\approx0.206$ a solution to $e^{iy}\cdot\left(e^{iy}+e^{-iy}\right)=e^{iy}\cdot\left(8ye^{4y^2}\right)$?

asked Nov 5, 2016 at 13:19

-2 votes

2 answers

79 views

Prove the inequality $(n-2k)^{2x}[2x+m(n-2k)]<2n^{2x}$

asked Sep 9, 2017 at 20:14

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13 Questions

Generalized series for $\pi$ - What is the polynomial?

Prove that $\sum_{i=1}^{n}\frac{1}{\left(n+i\right)^{2}}\sim\frac1{2n}$

Prove $4\sin^{2}\frac{\pi}{9}-2\sqrt{3}\sin\frac{\pi}{9}+1=\frac{1}{4}\sec^{2}\frac{\pi}{9}$.

Prove that the ratio of acute angles in a $3:4:5$ triangle is irrational

Can a function be well-defined on an integral of $\mathbb{R}$ but not Lebesgue integrable?

How did the Babylonians derive the Secant Method without algebra?

Simple definition for random polynomial $p:[0,1]\to[0,1]$

Is there any well defined $f:\mathbb{R}\to\mathbb{R}$, that is not the limit of any sequence of polynomials?

If $x^a<\ln(x)<x^b$, then how are $a$ and $b$ bounded?

Does $f_0=x,f_{n+1}(x)=e^{1/f_n(x)}$ converge to $1/W(1)$?

Can a power series with no constant equal a constant?

Is $y\approx0.206$ a solution to $e^{iy}\cdot\left(e^{iy}+e^{-iy}\right)=e^{iy}\cdot\left(8ye^{4y^2}\right)$?

Prove the inequality $(n-2k)^{2x}[2x+m(n-2k)]<2n^{2x}$