Question

what is the sum of the first 10,000 positive integers?

Answer 1

The sum of the first n positive integers can be easily found using Gauss' method.

$\sum\limits_{i=1}^n i=\dfrac{n(n+1)}{2}\\\\ \sum\limits_{i=1}^{10,000} i=\dfrac{10,000(10,000+1)}{2}\\ \sum\limits_{i=1}^{10,000} i=\dfrac{10,000 \cdot10,001}{2}\\ \sum\limits_{i=1}^{10,000} i=50,005$