The sum of the first n positive integers can be easily found using Gauss' method.
[tex]\sum\limits_{i=1}^n i=\dfrac{n(n+1)}{2}\\\\
\sum\limits_{i=1}^{10,000} i=\dfrac{10,000(10,000+1)}{2}\\
\sum\limits_{i=1}^{10,000} i=\dfrac{10,000 \cdot10,001}{2}\\
\sum\limits_{i=1}^{10,000} i=50,005[/tex]
