Economic growth is a very theoretical concept. Something doubles our economic growth if we make it and people value it as much as the stuff we are already making. If we invented new Japanese cartoon cat pens so cute and desirable that every person on the planet pays $1000 for it, bam! 7.1 trillion dollar growth. Just remove 7 billion regular pens to make room in the universe, and we're at 7.0999. (assuming no resources were diverted from other things)
Economic growth is kind of meaningless to think about at this scale. But at any two points on a more human scale, it means something.
That said, an exponentially growing (shoe) economy that eats the universe sounds like a Douglas Adams story so maybe you're right.
In the case of 1% growth the second interval is larger than the first, but the third is not larger than the first and second combined (it's still roughly 1/2 that).
It's certainly true that it won't be true for all interval lengths - that is obviously mathematically nonsensical.
In a finite universe, yes, it is clearly nonsense. Exponential growth cannot continue forever in a finite universe, no matter how small the growth constant.
I was saying you can't have growth for which f(n + k) = 2 f(n) for all k > 0 (I believe the only solution to that is f(n) = 0, which isn't what anyone is talking about when they talk about "exponential growth"...). This point was intended, in contrast with what I'd just said about there existing some k - to stress the notion of when the interval is picked.
Apparently, I wasn't doing it well, but that's what I was trying to do.
Whether unbounded exponential "economic growth" is possible in a finite universe is actually a significantly more involved question. It's obviously not possible if "economic value" is bounded, but in principle could be "possible" with finite stuff in continuous space (obviously, economic value depends significantly on configurations of stuff and not just amounts).
All of this is interesting, but I honestly don't expect any reasoning involving hard theoretic bounds to be of any use in determining what's likely over my lifetime, or those of my children.
Also, the primary problem is not really the growth itself, but the need for it that is built into the basic assumptions of economy - because if and when we'll eventually hit a speedbump, everything will collapse.