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=(n(n+1))/(2)\\\\ \sum\limits_(i=1)^(10,000) i=(10,000(10,000+1))/(2)\\ \sum\limits_(i=1)^(10,000) i=(10,000 \cdot10,001)/(2)\\ \sum\limits_(i=1)^(10,000) i=50,005`