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Matemática/1. Tópicos Fundamentais/Exercícios/Aritmética e Álgebra.md
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@@ -19,14 +19,23 @@ $$
2a_n = a_{n-1} + a_{n+1}
$$
$$
2a_2 = \dfrac{2}{\sqrt{c} + \sqrt{a}}
$$
$$
\begin{align*}
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
a_1 + a_2 &= \dfrac{1}{\sqrt{b}+\sqrt{c}} + \dfrac{1}{\sqrt{a}+\sqrt{b}} \\
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
&= \dfrac{(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} +
\dfrac{(\sqrt{b}+\sqrt{c})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} \\
\dfrac{1}{\sqrt{a_2} + \sqrt{a_3}}, \dfrac{1}{\sqrt{a_3} + \sqrt{a_1}}, \dfrac{1}{\sqrt{a_1} + \sqrt{a_2}} \\
&= \dfrac{(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} + \dfrac{(\sqrt{b}+\sqrt{c})}{(\sqrt{a}+\sqrt{b})(\sqrt{b}+\sqrt{c})} \\
&= \dfrac{\sqrt{a}+ 2\sqrt{b}+\sqrt{c}}{(\sqrt{a}\cdot+\sqrt{b})(\sqrt{b}+\sqrt{c})}
\end{align*}
$$
$$
= \dfrac{\sqrt{a}+ 2\sqrt{b}+\sqrt{c}}{(\sqrt{a}\cdot+\sqrt{b})(\sqrt{b}+\sqrt{c})}
$$