MathJax examples
To see how any formula was written right-click on the expression and choose "Show Math As > TeX Commands".
$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ $$\text{\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}}$$ $$\alpha, \beta, ..., \omega$$ $$\Gamma, \Delta, ..., \Omega$$ $$x_i^2$$ $$\log_2 x$$ $$10^{10}$$ $${x^y}^z$$ $$x^{y^z}$$ $$x_i^2$$ $$x_{i^2}$$ $$(2+3) \quad [4+4] \quad \{5+5\}$$ $$\left(\frac{\sqrt x}{y^3}\right)$$ $$(x) \quad [x] \quad \{x\} \quad |x| \quad \vert x \vert \quad \Vert x \Vert \quad \langle x \rangle \quad \lceil x \rceil \quad \lfloor x \rfloor$$ $$\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)$$ $$\sum_1^n \quad \sum_{i=0}^\infty i^2 \quad \prod_{i=0}^\infty i^2 \quad \int_{i=0}^\infty i^2 \quad \bigcup_{i=0}^\infty i^2 \quad \bigcap_{i=0}^\infty i^2 \quad \iint_{i=0}^\infty i^2$$ $$\frac ab \quad \frac{a+1}{b+1} \quad {a+1\over b+1}$$ $$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$$ $$\sqrt{x^3} \quad \sqrt[3]{\frac xy} \quad {\left(\frac xy\right)}^{1/2}$$ $$\lim x \quad \sin x \quad \ln x \quad \max(x,y) \quad \lim_{x\to 0} x$$ $$\lt \quad \gt \quad \le \quad \ge \quad \neq$$ $$\times \quad \div \quad \pm \quad \mp \quad \cdot$$ $$\cup \quad \cap \quad \setminus \quad \subset \quad \subseteq \quad \subsetneq \quad \supset \quad \in \quad \notin \quad \emptyset \quad \varnothing$$ $${n+1 \choose 2k} \qquad \binom{n+1}{2k}$$ $$\to \quad \rightarrow \quad \leftarrow \quad \Rightarrow \quad \Leftarrow \quad \mapsto$$ $$\land \quad \lor \quad \lnot \quad \forall \quad \exists \quad \top \quad \bot \quad \vdash \quad \vDash$$ $$\star \quad \ast \quad \oplus \quad \circ \quad \bullet$$ $$\approx \quad \sim \quad \simeq \quad \cong \quad \equiv \quad \prec \quad \lhd$$ $$\infty \quad \aleph_0 \quad \nabla \quad \partial \quad \Im \quad \Re$$ $$a\equiv b\pmod n$$ $$a_1, a_2, \ldots ,a_n \quad a_1+a_2+\cdots+a_n$$ $$\epsilon \quad \varepsilon \quad \phi \quad \varphi \quad \ell$$ $$\hat x \quad \widehat{xy} \quad \bar x \quad \overline{xyz} \quad \vec x \quad \overrightarrow{xy} \quad \overleftrightarrow{xy} \quad \frac d{dx}x\dot x = \dot x^2 + x\ddot x$$
$$\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}$$ $$\begin{pmatrix}1&2\\3&4\\ \end{pmatrix} \quad \begin{bmatrix}1&2\\3&4\\ \end{bmatrix} \quad \begin{Bmatrix}1&2\\3&4\\ \end{Bmatrix}$$ $$\begin{vmatrix}1&2\\3&4\\ \end{vmatrix} \quad \begin{Vmatrix}1&2\\3&4\\ \end{Vmatrix}$$ $$\begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots& \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \end{pmatrix}$$ $$\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]$$
$$\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align}$$ $$\begin{align} f(x)&=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\ f'(x)&=\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\\ f''(x)&=\left(6x+2\right)\\ \end{align}$$
$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$ $$\left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n)$$ $$f(n) = \begin{cases} \frac{n}{2}, & \text{if $n$ is even} \\[2ex] 3n+1, & \text{if $n$ is odd} \end{cases}$$
$$\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}$$ $$% outer vertical array of arrays \begin{array}{c} % inner horizontal array of arrays \begin{array}{cc} % inner array of minimum values \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & % inner array of maximum values \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} \\ % inner array of delta values \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} \end{array}$$
$$\begin{array}{ll} \hfill\mathrm{Bad}\hfill & \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}$$ $$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \{x|x^2\in\Bbb Z\} & \{x\mid x^2\in\Bbb Z\} \\ \end{array}$$ $$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \int\int_S f(x)\,dy\,dx & \iint_S f(x)\,dy\,dx \\ \int\int\int_V f(x)\,dz\,dy\,dx & \iiint_V f(x)\,dz\,dy\,dx \end{array}$$ $$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ \iiint_V f(x)dz dy dx & \iiint_V f(x)\,dz\,dy\,dx \end{array}$$
$$\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.$$ $$\begin{cases} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{cases}$$ $$\left\{\begin{aligned} a_1x+b_1y+c_1z&=d_1+e_1 \\ a_2x+b_2y&=d_2 \\ a_3x+b_3y+c_3z&=d_3 \end{aligned} \right.$$ $$\left\{\begin{array}{ll}a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y &=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{array} \right.$$ $$\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex] a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex] a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}$$ $$\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\ a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\ a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}$$ $$\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\ [2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.$$
$$\require{cancel}\begin{array}{rl} \verb|y+\cancel{x}| & y+\cancel{x}\\ \verb|\cancel{y+x}| & \cancel{y+x}\\ \verb|y+\bcancel{x}| & y+\bcancel{x}\\ \verb|y+\xcancel{x}| & y+\xcancel{x}\\ \verb|y+\cancelto{0}{x}| & y+\cancelto{0}{x}\\ \verb+\frac{1\cancel9}{\cancel95} = \frac15+& \frac{1\cancel9}{\cancel95} = \frac15 \\ \end{array}$$ $$\require{enclose}\begin{array}{rl} \verb|\enclose{horizontalstrike}{x+y}| & \enclose{horizontalstrike}{x+y}\\ \verb|\enclose{verticalstrike}{\frac xy}| & \enclose{verticalstrike}{\frac xy}\\ \verb|\enclose{updiagonalstrike}{x+y}| & \enclose{updiagonalstrike}{x+y}\\ \verb|\enclose{downdiagonalstrike}{x+y}| & \enclose{downdiagonalstrike}{x+y}\\ \verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| & \enclose{horizontalstrike,updiagonalstrike}{x+y}\\ \end{array}$$
$$x = a_0 + \cfrac{1^2}{a_1 + \cfrac{2^2}{a_2 + \cfrac{3^2}{a_3 + \cfrac{4^4}{a_4 + \cdots}}}}$$ $$\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}.$$
$$\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}$$ $$(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)$$ $$\underbrace{a\cdot a\cdots a}_{b\text{ times}}$$ $$\check{I} \quad \acute{J} \quad \grave{K}$$
$$\require{AMScd} \begin{CD} A @>a>> B\\ @V b V V= @VV c V\\ C @>>d> D \end{CD}$$ $$\begin{CD} A @>>> B @>{\text{very long label}}>> C \\ @. @AAA @| \\ D @= E @<<< F \end{CD}$$ $$\begin{CD} RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}>> (RCOR')+NaCl+SO_2+ H_2O \end{CD}$$