Argue with the high school teacher.
The integers are closed under multiplication (if you multiply two integers, you get another integer), but they are _not_ closed under division, since you can divide two integers to get a rational number that isn't an integer.
The rationals, however, are closed under addition, subtraction, multiplication, and division.
Maybe the tilt came when you looped your summation to infinity. I don't know. Maybe the Mathematician can tell us.
So you don't know what that little "sideways eight" atop the sigma symbol means? Sad.
Your equation included more operations than just addition, subtraction, multiplication and division, under which the set of rationals is indeed closed. It included the operation of infinite summation under which the set of rationals is most definitely NOT closed. Any infinite, nonrepeating decimal is an example of an infinite summation of rationals that yields an irrational result, for example.