Multi-line Equations

Often, in a derivation, you will want to have a series of equations or inequalities aligned together. Surround the equations by \begin{eqnarray*} and \end{eqnarray*}. (The same command without the asterisk generates equation numbers automatically.) Surround the equals sign or inequality with &'s, and end each line with \\. Note: you do not need to use $$'s with this environment. For example,

\begin{eqnarray*}
1+2+\ldots+n &=& \frac{1}{2}((1+2+\ldots+n)+(n+\ldots+2+1))\\
&=& \frac{1}{2}\underbrace{(n+1)+(n+1)+\ldots+(n+1)}_{\mbox{$n$ copies}}\\
&=& \frac{n(n+1)}{2}\\
\end{eqnarray*}

produces

$$\begin{eqnarray*} 1+2+\ldots+n &=& \frac{1}{2}((1+2+\ldots+n)+(n+\ldots+2+1)) ... ...1)+\ldots+(n+1)}_{\mbox{$n$ copies}}\\ &=& \frac{n(n+1)}{2}\\ \end{eqnarray*}$$

Practice: Produce your own aligned set of 5 equations.