The first 100 positive even numbers are 2; 4; 6;...; 200. Their sum is \(\dfrac{\left(200+2\right).100}{2}=10100\).
The first 100 positive odd numbers are 1; 3; 5;...; 199. Their sum is \(\dfrac{\left(199+1\right).100}{2}=10000\)
The difference between two sums is \(10100-10000=100\)