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1. 2. Some examples. For any positive real numbers $a,b,c$ we have $$\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3.$$ This inequality follows from the following inequality: \begin{equation} x+y+z\ge 3\sqrt{xyz} \forall x,y,z\ge 0. \label{eq:amgm} \end{equation} The inequality \eqref{eq:amgm} is the well-known AM-GM inequality. Results: For any positive real numbers $a,b,c$ we have $$\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge 3.$$ This inequality follows from the following inequality: \begin{equation} x+y+z\ge 3\sqrt{xyz}\quad \forall x,y,z\ge 0. \label{eq:amgm} \end{equation} The inequality \eqref{eq:amgm} is the well-known AM-GM inequality.
3. We have $\LaTeX$ support on the forum. Almost all of the basic $\LaTeX$ commands are supported, so just type as you do in a $\LaTeX$ document. Examples are given in the next posts. In addition, there is a built-in equation editor to make life easier Press the $\mathbf{f_x}$ button on the text editor toolbar and try.