the sum of the first 10000 positive even numbers is how much more than the sum of the first 10000 positive odd numbers?
10000 more......
To see this, look at the sum of the first five positive even numbers
2 + 4 + 6 + 8 + 10 = 30
And look at the sum of the first five positive odd numbers
1 + 3 + 5 + 7 + 9 = 25
The difference between the two sums is 5. This leads us to believe that the difference between the sum of the first n positive even numbers and the first n positive odd numbers is just n.
10000 more......
To see this, look at the sum of the first five positive even numbers
2 + 4 + 6 + 8 + 10 = 30
And look at the sum of the first five positive odd numbers
1 + 3 + 5 + 7 + 9 = 25
The difference between the two sums is 5. This leads us to believe that the difference between the sum of the first n positive even numbers and the first n positive odd numbers is just n.