You are right and I am glad I didn't write 'because Maths'. The sum you're quoting from is monotonically growing but at an ever shrinking clip. However, the series does not describe the kind of growth that our economy seemingly needs and our politicians like to promise, nor does it AFAICS describe the OP's idea of continued population growth given his recommendation to shun shrinking populations with fertility below replacement rate; theirs is a constant or in the midterm increasing growth and notwithstanding [minority opinions](https://www.youtube.com/watch?v=w-I6XTVZXww) claiming that 1 + 2 + 3 + 4 + 5 + ... equals -1/12 such a series cannot have a finite sum, hence is physically unfeasible to represent.