I think there will be other perceptions on how to view the subject, one way or another.
Looking at it as a form of a series is one of those views. It is a form of series, anyways. ._.
>>35
Both are series of numbers. Their ratio of the the two consecutive terms works the same.
>>30
Huh, whut? On number two. What is with the adding 0.9/10^n where n is a positive integer approaching infinity thingy? Is this what you meant?(but if you want it to work in there, the value of n must be a zero to represent the first term and going towards a positive integer when going up to infinity): 0.999... = 0.9+0.09+0.009+...+0.9/10^n, but the last part that you wanted to add is really not necessary. Anybody with a mathematical inclination can see that it's a fixed series/sequence of numbers without the extra appendage.
0.99999... is not a solid and concrete quantity, in my opinion. Can you write the number down in its entirety? I certainly can't. It's a geometric sum too. A sum that works its way up geometrically in sequence where the number of terms is approaching infinity. 0.999... = 0.9+0.09+0.009+...+0.9/10^n(Really, I don't think it's necessary).
I don't know how to modify post, if there is a function like that in here anyways... so, yes. When the number of the geometric terms(or however you may call it) reaches infinity(which is the limit, as you said), it'll be 1 when summed together(a finite number), not approach 1. My apologies, I was too lazy to clarify myself, and I suck at explaining what I mean. I will get my terminology wrong many times.