Using MimeTeX 3

Brackets

As students advance through Maths, they come into contact with brackets. Algebraic notation depends heavily on brackets. The usual keyboard values of ( and ) are useful, for example:

  $d=2\ \times \ (4\ -\ j)$

This is written as:

 $$ d = 2 \ \times \ (4 \ - \ j) $$

Usually, these brackets are enough for most formulae but they will not be in some circumstances. Consider this:

 $4x^{3}\ +\ (x\ +\ {\frac {42}{1+x^{4}}})$ 

Is OK, but try it this way:

 $4x^{3}\ +\ \left(x\ +\ {\frac {42}{1+x^{4}}}\right)$ 

This can be achieved by:

 $$ 4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right) $$

A simple change using the \left( and \right) symbols instead. Note the actual bracket is both named and presented.

Ellipsis

The Ellipsis is a simple code:

$$ x_1, \ x_2, \ \ldots, \ x_n $$

Written like:

\$\$ x_1, \ x_2, \ \ldots, \ x_n \ \$\$

A more practical application could be:

Question: "Add together all the numbers from 1 $$ \ \ldots \ $$ 38. What is an elegant and simple solution to this problem? Can you create an algebraic function to explain this solution? Will your solution work for all numbers?"

Answer: The question uses an even number to demonstrate a mathematical process and generate an algebraic formula.