I have failed to find a relevant question, so I am posting one. As the question says, is $2+2+2+\dotsb$ even or odd? Or since this "number" is not an integer, it might be undefined.
Furthermore, are the following two expressions equivalent?
$$1+1+1+\dotsb = 1+(1+1)+(1+1+1)+\dotsb$$
Now "$+$" is an associative binary operation, but I have a scratchy feeling they should not be the same because of the idea of infinity. Lastly, I want to know more about (absolutely or conditionally) divergent series, and is there a good reference I can look into? Thank you in advance.