I would almost certainly need that. To display the result up to a certain accuracy, I assumed in the code above that the distance between two consecutive terms gets smaller and smaller. It's always possible to find a subsequence with such a property so we can define all reals as such.
I'm not sure this property is conserved with the arithmetic operations as defined above. So I would need a rigorous way of dealing with the sum or product of terms whose precision is known up to a given accuracy.
So: thanks, that'll be useful if I ever want to implement this thing for real.