First point of contention: 0.99999... is approximately equal to one.
Draw a number line and place exactly where 0.99999... is. If its approximately equal to 1, how close would you place it to the number 1? One may think that the number moves closer and closer to 1 but never reaches there; however this is not the case. Since 0.99999... is a fixed number and not a sequence/series, it will not move on the number line, which brings me to my next point.
Second point of contention: 0.99999... as a geometric sequence/series.
You're not adding (0.9)/10^n where n is 1,2,3... to this number an infinite number of times. That is nonsensical. The number 0.99999... is a concrete and fixed quantity, not a sequence. Since the number extends infinitely, it is EQUAL to its limit, not "approaching" it. The limit in this case happens to be 1.