sequences and series - Why does $1+2+dots+2003=dfrac{2004cdot2003}2$?

Why does $1+2+\dots+2003=\dfrac{2004\cdot2003}2$?

Sorry if this is missing context; not really much to add...

Answer

$$\begin{array}{ccc}
S&=&1&+&2&+&3&+&\ldots&+&2001&+&2002&+&2003\\
S&=&2003&+&2002&+&2001&+&\ldots&+&3&+&2&+&1\\ \hline
2S&=&2004&+&2004&+&2004&+&\ldots&+&2004&+&2004&+&2004
\end{array}$$

There are $2003$ columns, so $2S=2003\cdot2004$, and therefore $S=\dfrac{2003\cdot2004}2$.