f:\mathbb{N}\to\mathbb{Z}

$\mathbb{Q} \mathbb{Q}_+ $
$\R \R_-^* $

$\underbrace{1+2+...+n}_{\mbox{n termeni}}=\frac{n(n+1)}{2}$

$$\underbrace{1^2+2^2+...+n^2}_{n\text{ termeni}}=\dfrac{n(n+1)(2n+1)}{6}$$

$ A \in \mathcal{M}_3(\C)$

Fie

$ A =\begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33} \\
\end{pmatrix}$

$ detA =\begin{vmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33} \\
\end{vmatrix}$

Sume

1+2+\dots+n=\displaystyle\sum_{k=1}^{n}k

Produse

1\cdot 2\cdot...\cdot n=n!=\displaystyle\prod_{k=1}^{n}k

Integrale

$\displaystyle\int\sqrt{\ln^2{(\sin{x})}}dx$

$\displaystyle\int_{\frac{\pi}{2}}^{\pi}\arctg{x}dx$

Limite

$\displaystyle\lim_{ \alpha \to\infty}\frac{\alpha^2+1}{ \alpha^2-1 }=1$

$\sqrt[3]{x}=x^\frac{1}{3}$

$\sqrt[3]{\sqrt[5]{\sqrt[7]{...\sqrt[2k+1]{\psi}}}}$

$\displaystyle\sqrt[3]{\sqrt[5]{\sqrt[7]{...\sqrt[2k+1]{\psi}}}}$

Constanta lui Euler

$C=-\displaystyle\int_{0}^{\infty}e^{-t}\lntdt$

$C\approx 0,577 \simeq 0,577215664$

$C=\displaystyle\lim_{n\to\infty}\displaystyle\left(\sum_{k=1}^{n-1}\frac{1}{k}-\lnn\right)$

Teorema (Inegalitatea lui Jensen)

Daca

este convexa si

cu

,atunci:

Inegalitatea lui Cauchy-Holder

$\displaystyle\sum_{i=1}^{n}a_ib_i\le\displaystyle\left(\sum_{i=1}^{n}b_i^\frac{k}{k-1}\right)^\frac{k-1}{k}\cdot\left(\sum_{i=1}^{n}a_i^k\right)^\frac{1}{k}$