>>"The mass of the fuel does increase, but why do you forget that the mass of your rocket also increases with it, hence, more fuel is required for it's acceleration.
Overall, the relative proportion remains the same."
Relative to the crew, the rockets proportions have not changed, so why should its ability to accelerate? What stops it reaching light speed?
EDIT: Now I see Clyde has changed the 'not enough energy in the universe to reach light speed post'.