# Simple Examples

  Embedded in {$\sqrt{x^2 + 2xy + y^2}$} text  Embedded in \sqrt{x^2 + 2xy + y^2} text 
  Centered {$$\sqrt{x^2 + 2xy + y^2}$$}  Centered \sqrt{x^2 + 2xy + y^2} 
  {$${1\over 2} \quad {n+1\over 3} \quad {n+1 \choose 3} \quad \sum_{n=1}^3 Z_n^2$$}   {1\over 2} \quad {n+1\over 3} \quad {n+1 \choose 3} \quad \sum_{n=1}^3 Z_n^2 
  {$${\textstyle \sum x_n}\quad {\sum x_n} \quad \sum_{n=1}^m x_n^2$$}   {\textstyle \sum x_n}\quad {\sum x_n} \quad \sum_{n=1}^m x_n^2 

For some reason the built-in demonstration markup does not interpret correctly the expression under the integral droping dt one line. However, no everything is lost. Outside the demonstration markup the integral comes out right: \int_0^\infty f(t)\,dt . You can see the corresponding LaTex code by clicking on that expression.

 {$$\sqrt{2} = \sup \left\{ x\in\mathbb{Q}: x^{2}<2\right\}$$} \sqrt{2} = \sup \left\{ x\in\mathbb{Q}: x^{2}<2\right\}

Would you guess it:

  {$$2 = \sqrt{2+\sqrt{2+\sqrt{2+ ....}}}$$}  2 = \sqrt{2+\sqrt{2+\sqrt{2+ ....}}} 

And this is how you get the Taylor series:

  {$$f(u_1) = f(u_0) + hf'(u_0)+{h^2\over 2!}f''(u_0) + \cdots + {h^{n+1}\over (n+1)!}f^{(n+1)}(u_0) + o(h^{n+1}).$$}   f(u_1) = f(u_0) + hf'(u_0)+{h^2\over 2!}f''(u_0) + \cdots + {h^{n+1}\over (n+1)!}f^(n+1)(u_0) + o(h^{n+1}).