Example Page

$f(x)=x^{2}$

$f(x)\,\!$ $=\sum _{n=0}^{\infty }a_{n}x^{n}$ $=a_{0}+a_{1}x+a_{2}x^{2}+\cdots$

$\left({\frac {1}{2}}\right)^{n}$

$x={\frac {{\color {Blue}-b}\pm {\sqrt {\color {Red}b^{2}-4ac}}}{\color {Green}2a}}$

$\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}$

$|{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)$

${\begin{aligned}\overbrace {{\ce {2Fe3O4}}} ^{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Brown}\overbrace {{\ce {3(\lambda{-}Fe2O3)}}} ^{\text{maghemite}}}\\\underbrace {{\ce {2Fe3O4}}} _{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Red}\underbrace {{\ce {3(\alpha{-}Fe2O3)}}} _{\text{hematite}}}\end{aligned}}$

$x^{2}+y^{2}+z^{2}=1$

(1)

Eq. 1 $x^{2}+x+1=0$

$f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}$

$\left({\begin{array}{cc}a&b\\c&d\end{array}}\right)$

Image Test

${\begin{aligned}\int \ln(x)^{3}dx=x\ln(x)^{3}-3\int \ln(x)^{2}dx\end{aligned}}$