### Instruction: What is the ratio of the sum of the odd integers between 0 and 100, to the sum of the odd integers between 100 and 200? Express your answer as a common fraction.### Response: To find the sum of the odd integers between 0 and 100, I can use a formula for the sum of an arithmetic series.
The first term is 1, the last term is 99, and the common difference is 2.
The number of terms is (99 - 1) / 2 + 1 = 50.
So the sum is 50 * (1 + 99) / 2 = 2500.
Similarly, to find the sum of the odd integers between 100 and 200, I can use the same formula.
The first term is 101, the last term is 199, and the common difference is 2.
The number of terms is (199 - 101) / 2 + 1 = 50.
So the sum is 50 * (101 + 199) / 2 = 7500.
Therefore, the ratio of the two sums is 2500 / 7500 = 1 / 3.