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\title{Exercise in mathematical formulae in LATEX }
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The solutions of a quadratic equation $a x^{2}+b x+c=0$ are given by the formulae
$$
x_{1}=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a} \quad \text { and } \quad x_{2}=\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}
$$
The set $\left\{x\right.$ such that $\left.x^{2} \geq 9\right\}$ is equal to the set $(-\infty ;-3] \cup[3 ; \infty)$.
A finite sum of a geometric progression
$$
a_{0}+r a_{0}+r^{2} a_{0}+r^{3} a_{0}+\cdots+r^{k} a_{0}
$$
with ratio $r \neq 1$ is equal to
$$
\sum_{i=0}^{k} r^{i} a_{0}=a_{0}\left(\frac{1-r^{k+1}}{1-r}\right)
$$
The infinite sum of a geometric progression
$$
a_{0}+r a_{0}+r^{2} a_{0}+r^{3} a_{0}+\cdots
$$
with ratio $r$ satisfying $0<r<1$ is equal to
$$
\sum_{i=0}^{\infty} r^{i} a_{0}=\frac{a_{0}}{1-r}
$$
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