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Mathematics
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Adam Boussif's user avatar
Adam Boussif's user avatar
Adam Boussif
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6
Evalaute $\sum_{k=1}^\infty \arctan \left(\frac{1}{1+3k+k^2}\right)$
Oct 11, 2023
3
equality involving supremum and infimum of two disjoint sets that partition the real Line
Jul 7
2
A railroad track connects a station A to another K passing successively through stations from A to K
Mar 10, 2022
2
Help me solve this inequality :$\forall x,y,z > 0 : \sum\limits_{cyc} \frac{x}{xz+2x+1} \leq \frac{3}{4}$ [duplicate]
Jul 23, 2022
2
Inequality with smoothing technique:$\sum_{i=1}^{n}\frac{x_{i}}{\sqrt{1-x_{i}}}\geq \sqrt{\frac{n}{n-1}}$ subject to $\sum_{i=1}^{n} x_{i}=1 $
Aug 22, 2022
2
Proving a quartic has exactly one positive real solution
Jun 24, 2023
1
Show that $\forall k,j,m,n \in \mathbb{N}^: 3kn^2 +3jn +3m+2 \notin S=\{x^2 \mid x\in \mathbb{N}\}$
Jul 24, 2022
1
If a, b, c are positive real numbers such that $a^2+ b^2+ c^2 = 1$ $( \frac{1}{a} +\frac{1}{b} +\frac{1}{c}) +a +b +c \geq 4\sqrt{3}$
Jul 27, 2022
1
Prove $\frac{x}{y^2}+\frac{y}{z^2}+\frac{z}{x^2}\geq x^3+y^3+z^3$ where $x,y,z>0$ and $x+y+z=3$.
Aug 14, 2022
1
For all natural numbers $a_i$ of the set $\{1,2,\dots\,2017\}$ show that $\sum_{i=1}^{2017}\frac{{a_i}^2-i^2}{i} \geq 0$
Nov 28, 2022