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.

Cute counterexample, I'll grant you that, but the parent posts were – if implicitly – talking abound unbounded growth.

Bounded growth on the other hand might mathematically indeed continue for an infinite length of time, but for all practical purposes can most certainly be rounded down to zero past a certain point.

But that's not our growth. Our system suppose constant exponential growth. And to use your maths:

1% + 0.5% + 0.25% + 0.125%....

Is this sequence constant growing? Yes. Is this sequence infinitely increasing? Yes. Does this sum up to a finite value? _Sadly no_

I'd have to brush up on my math but even that feels bounded. Per cent is just division by 100, you take it out as a common divisor and you still arrive at the same sum.

Unless you mean something like

  1 * 1.01 * 1.02 * 1.03.....

Which is indeed unbounded.