When calculating infinite sums, if and when applicable can you cancel out the variables to equal zero?
For example:
if I was trying to solve the infinite sum of this equation: $$\{x + y + (-x) + (-y)\} + \cdots,$$ where $\{\}$ repeats infinitely, could I use a cancelling out method to cancel out $x$ and $y$ from the equation, and therefore making the sum of the infinite series equal to $0\,$?
Can I do this?