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Iuli
  • Member for 11 years, 11 months
  • Last seen more than a month ago
  • Timisoara, Romania
43 votes
8 answers
4k views

Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$

23 votes
2 answers
1k views

Trigonometric Inequality. $\sin{1}+\sin{2}+\ldots+\sin{n} <2$ .

21 votes
4 answers
3k views

prove that $10200300040000100004000300201$ is not perfect square

19 votes
6 answers
5k views

Inequality. $\frac{1}{16}(a+b+c+d)^3 \geq abc+bcd+cda+dab$

16 votes
2 answers
2k views

Inequality. $\sqrt{\frac{11a}{5a+6b}}+\sqrt{\frac{11b}{5b+6c}}+\sqrt{\frac{11c}{5c+6a}} \leq 3$

15 votes
4 answers
1k views

Inequality $a+b+c \geqslant abc +2$

15 votes
6 answers
3k views

Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor

15 votes
4 answers
14k views

Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$

12 votes
2 answers
9k views

When is the image of a linear operator (between Banach spaces) closed?

10 votes
3 answers
1k views

Proving inequality $\frac{a}{\sqrt{a+2b}}+\frac{b}{\sqrt{b+2c}}+\frac{c}{\sqrt{c+2a}}\lt \sqrt{\frac{3}{2}}$

9 votes
8 answers
3k views

Inequality. $a^2+b^2+c^2 \geq a+b+c$ [closed]

9 votes
3 answers
2k views

A inequality proposed at Zhautykov Olympiad 2008

9 votes
1 answer
5k views

about closed linear subspace

8 votes
3 answers
670 views

Matrix Equation $A^3-3A=\begin{pmatrix}-7 & -9\\ 3 & 2\end{pmatrix}$

7 votes
2 answers
6k views

Limit. $\lim_{n \to \infty}\frac{1^p+2^p+\ldots+n^{p}}{n^{p+1}}$. [duplicate]

7 votes
1 answer
1k views

Inequality. $abc(a+b+c) > 3abc+ab+bc+ca.$

7 votes
2 answers
897 views

about the following sum : $\frac{1}{1 \cdot 3}+\frac{2}{1 \cdot 3 \cdot5}++\ldots+\frac{n}{1 \cdot 3 \cdot 5 \cdot7 \cdot \ldots \cdot (2n+1)}$

7 votes
4 answers
244 views

$5^{2012}+1$ is divisible with $313$

7 votes
1 answer
443 views

The solutions for the equation $\frac{a}{c-b+1}+\frac{b}{a-c+1}+\frac{c}{b-a+1}=0.$

6 votes
1 answer
252 views

Infinitesimal Transformation. Importance of Infinitesimal Transformation

6 votes
1 answer
87 views

how to compute a differential?

6 votes
0 answers
84 views

(History) Books About Geometry of Curves and Surfaces

6 votes
4 answers
2k views

Books on functional equations

6 votes
2 answers
2k views

Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$

6 votes
3 answers
1k views

Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

6 votes
1 answer
238 views

Inequality. $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}+\frac{3n}{a^2+b^2+c^2} \geq 3+n$

6 votes
4 answers
9k views

Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$

6 votes
2 answers
584 views

Inequality. $\frac{1}{\sqrt{x^2+yz+3}}+\frac{1}{\sqrt{y^2+zx+3}}+\frac{1}{\sqrt{z^2+xy+3}} \geq 1$

6 votes
7 answers
475 views

Inequality. $\frac{a}{\sqrt{b}}+\frac{b}{\sqrt{c}}+\frac{c}{\sqrt{a}}\geq3$

6 votes
2 answers
266 views

Calculate or approximate $\sum\limits_{k=801}^{849}{ \binom {2400} {k}} $

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