Eclipse Sun's user avatar
Eclipse Sun's user avatar
Eclipse Sun's user avatar
Eclipse Sun
  • Member for 10 years, 1 month
  • Last seen more than a month ago
45 votes

'Bee flying between two trains' problem

26 votes

What is the $1469^\text{th}$ derivative of $x^{532}-5x^{37}-4$?

23 votes

How can you prove that $1+ 5+ 9 + \cdots +(4n-3) = 2n^{2} - n$ without using induction?

22 votes
Accepted

How prove $\pi^2>2^\pi$

18 votes

Is there a logarithm base for which the logarithm becomes an identity function?

15 votes

Example of convergence in distribution but not in probability

13 votes
Accepted

Variations of $\lim_{n\rightarrow \infty} \left(1 + \frac{1}{n}\right)^n$

12 votes
Accepted

Taking the square root of an imaginary number

11 votes
Accepted

Calculate $\lim \limits_{x \to \infty} x\int_{0}^{x}e^{t^2-x^2}dt$

8 votes
Accepted

How to calculate the determinant of this matrix?

7 votes
Accepted

Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$

7 votes
Accepted

How to get this equation solved?

7 votes

Prove that $\mathbb{Q}{[\sqrt3]} = \lbrace a + b\sqrt3: a, b \in \mathbb{Q} \rbrace$ is a subfield of $\mathbb{R}$

7 votes
Accepted

Show that $\ln\left(1+3x + 2x^2\right) = 3x - \frac{5x^2}{2} + \frac{9x^3}{3} -\cdots + \left(-1\right)^{n-1}\frac{2^n+1}{n}x^n+\cdots$

7 votes
Accepted

Convergence of $\sum_{n=1}^\infty\left(\frac{1}{a_n^2}-\frac{1}{a_{n+1}^2}\right)$ where $a_1=1$ and $a_n=2-\frac 1n$ for $n\geq 2$

6 votes

Find $n \times n$ matrices $A$ such that $\det A = 0$ and $\text{rank}(AB) = \text{rank}(BA)$ for any $n \times n$ matrix $B$

6 votes

Show that the ring of polynomials with coefficients in a field, and in infinitely many variables, is not Noetherian

6 votes
Accepted

Limits in multivariable functions

6 votes
Accepted

How do you calculate $\lim_{z\to0} \frac{\bar{z}^2}{z}$?

6 votes

About Integration $\int_{-\infty}^{\infty} e^{-x^2} \cos(x^2) dx$

6 votes

Does $\int_{0}^1\frac{\ln(1+x+x^2)}{x}\mathrm dx$ have a closed form?

6 votes
Accepted

find the limit for Integral

5 votes
Accepted

Equivalence to being a topological group

5 votes
Accepted

A function is continuous if and only if its composition with the inclusion map is continuous.

5 votes

Why does squaring of the radius of a circle times pi give us the area?

5 votes
Accepted

Does every plane curve contain a rational point?

5 votes
Accepted

Trigonometry question

5 votes
Accepted

Show that the series $\sum_{n=3}^{\infty} n(\log n)(\log {\log n})^2 a_n$ diverges.

5 votes
Accepted

What does $\mathbb{C} / \mathbb{Z}$ mean?

5 votes
Accepted

Is it meaningful to distinguish a one-object category and its opposite?

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