cele 24 reguli fundamentale la a fi un sigma
<tex> regula sigma 1: sol_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2\cdot a} </tex>

cele 11 reguli fundamentale la a fi un sigma
<tex> regula sigma 1: \text{sol}_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2\cdot a} </tex>

<tex> regula sigma 2: f'(c)=\frac{f(a) - f(b)}{a - b} </tex>
<tex> regula sigma 3: C_n=\frac{1}{n + 1} \cdot \binom{2 \cdot n}{n} </tex>
<tex> regula sigma 4: \sum^{n}_{1}i = \frac{n \cdot (n + 1)}{2}  </tex>

<tex> regula sigma 7: \frac{2}{\frac{1}{a} + \frac{1}{b}} \leq \sqrt{a \cdot b} \leq \frac{a + b}{2} \leq \sqrt{\frac{a^2 + b^2}{2}}</tex>
<tex> regula sigma 8: \frac{AC}{CD} = \frac{AB}{BD}, \Delta ABC \text{ cu } \angle BAD = \angle DAC  </tex>
<tex> regula sigma 9: \sum^{n}_{0}\binom{n}{i} = 2^n</tex>

<tex> regula sigma 10: AH = 2R \cdot \cos{A}</tex>

<tex> regula sigma 10: AH = 2R \cdot \cos{a}</tex>

<tex> regula sigma 11: A = i + \frac{p}{2} + 1 </tex>

<tex> regula sigma 12: (\sum^{n}_{1}{a_i \cdot b_i}) ^ 2 \leq (\sum^{n}_{1}{a_i ^ 2})\cdot (\sum^{n}_{1}{b_i ^ 2})</tex>
<tex> regula sigma 13: \sum^{n}_{1}{\frac{a_i ^ 2}{b_i}} \geq \frac{ (\sum^{n}_{1}{a_i} ^ 2) }{\sum^{n}_{1}{b_i}}</tex>
<tex> regula sigma 14: \zeta(s) = \sum^{\infty}_{1}{n^s} </tex>
<tex> regula sigma 15: \binom{n}{k} = \frac{n!}{(n-k)! \cdot k!}</tex>
<tex> regula sigma 16: f(\sum^{n}_{1}{p_i x_i}) \leq \sum^{n}_{1}{p_i \cdot f(x_i)}</tex>
<tex> regula sigma 17: f_n = \frac{(\frac{1 + \sqrt{5}}{2}) ^ n - (\frac{1 - \sqrt{5}}{2}) ^ n}{\sqrt{5}}</tex>
<tex> regula sigma 18: P(|X - \mu| \geq k \sigma) \leq \frac{1}{k^2}</tex>
<tex> regula sigma 19: \sum_{cyc}{x^t(x-y)(x-z) \geq 0}</tex>
<tex> regula sigma 20: a ^ {p - 2} \equiv \frac{1}{a} (\text{mod }p)</tex>
<tex> regula sigma 21: (n - 1)! \equiv -1(\text{mod }n)</tex>
<tex> regula sigma 22: \binom{m}{n} = \prod^{k}_{1}{\binom{m_i}{n_i}} \text{  (mod p)}</tex>
<tex> regula sigma 23: (\sum^{n}_{1}{(a_k + b_k) ^ p})^{\frac{1}{p}} \leq (\sum^{n}_{1}{a_k^p}) ^{\frac{1}{p}} + (\sum^{n}_{1}{b_k^p}) ^{\frac{1}{p}} </tex>
<tex> regula sigma 24: \sum^{n}_{1}{a_i b_i} \leq (\sum^{n}_{1}a_i^p)^{\frac{1}{p}} + (\sum^{n}_{1}b_i^q)^{\frac{1}{q}} </tex>
<tex> regula sigma 25: \frac{f(a) - f(b)}{g(a) - g(b)} = \frac{f(c)}{g(c)}</tex>
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