Skip to main content
Guy Fsone's user avatar
Guy Fsone's user avatar
Guy Fsone's user avatar
Guy Fsone
  • Member for 7 years, 7 months
  • Last seen this week
48 votes

Probability that two random numbers are coprime is $\frac{6}{\pi^2}$

39 votes
Accepted

Is a Lipschitz function differentiable?

34 votes
Accepted

For each $a \in \mathbb{R}$ evaluate $ \lim\limits_{n \to \infty}\left(\begin{smallmatrix}1&\frac{a}{n}\\\frac{-a}{n}&1\end{smallmatrix}\right)^n$

30 votes
Accepted

Proof only by transformation that : $ \int_0^\infty \cos(x^2) dx = \int_0^\infty \sin(x^2) dx $

19 votes
Accepted

Sum of odd terms of a binomial expansion: $\sum\limits_{k \text{ odd}} {n\choose k} a^k b^{n-k}$

16 votes
Accepted

Why can complex numbers be written in exponential form? $z=r(\cos \theta+i\sin \theta)$ is $z=re^{i\theta}$.

13 votes
Accepted

If $\sum\limits_{n=1}^\infty a_n $converges does it imply that $\sum\limits_{n=1}^\infty \dfrac {a_n^{1/4}}{n^{4/5}}$ is convergent?

11 votes

Integral of periodic function over the length of the period is the same everywhere

11 votes

Matrix raised to a matrix: $M^N$, is this possible? with $M,N\in M_n(\Bbb K).$

10 votes

Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$

10 votes
Accepted

Find $x\in \Bbb R,$ solving $x=\sqrt{1+\sqrt{1+\sqrt{1+x}}}$

10 votes

Showing that $\lvert H K\rvert = \frac{| H\| K|}{ |H\cap K|}$

10 votes
Accepted

What is the closed form of the sequence : $ a_{n+2} = 2a_{n+1}-a_n+2^n+2 $

9 votes
Accepted

Is the cartesian product of two Hilbert spaces a Hilbert space?

9 votes
Accepted

It is possible to write open subsets in the form $\Omega=\{x\in \mathbb{R}^N:g(x)>0 \}$

9 votes

Minimize $\min_{f\in E}\left(\int_0^1f(x) dx\right)$

8 votes

Symmetric-decreasing rearrangement of a function

8 votes
Accepted

Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$

8 votes

Assume $\alpha, \beta \in \Bbb C,$ such that $\alpha^m = \beta^n = 1$ show that $(\alpha+\beta)^{mn}\in \Bbb R$

8 votes

Prove that the Gaussian Integer's ring is a Euclidean domain

8 votes

Proving that $x - \frac{x^3}{3!} < \sin x < x$ for all $x>0$

7 votes
Accepted

Integrating $\int_{0}^{1} x^a (c-x)^b dx $

7 votes

Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$.

7 votes

Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?

7 votes
Accepted

If $p\in\Bbb Z[X]$ show that: $ \max\limits_{x\in [0,1]}\left|p(x) \right| > \frac{1}{e^{n}}. $

7 votes

Prove $\sin^2 \theta +\cos^4 \theta =\cos^2 \theta +\sin^4 \theta $

7 votes

If all proper subsequences converge to same limit then the sequence converges.

7 votes
Accepted

Does this serie $\sum\limits_{n=0}^{\infty}\left(\frac{n}{n+1}\right)^{n^2}$ converge?

7 votes
Accepted

I noticed a relation between the cosines of $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $90^\circ$ and the square roots of $4, 3, 2, 1, 0$

7 votes

MIT Integration Bee 2017 problem:$\int_0^{\pi/2}\frac 1 {1+\tan^{2017} x} \, dx$ : Need hints

1
2 3 4 5
28