If you paid attention earlier, the formula works in single frames of time. Therefore it is appropriate to do a case for every second.

Now how about you try and figure out how long it takes us to reach the speed of lights starting at u=0.

No, the formula does not work in single frames of time, and it is not appropriate to do a case for every second. Please cite a source that says that it is.

No, I'm not going to do your math for you.

I can help you a little bit with the mathematical problem here. Inside a humongous mass of garbage, EnglshGentleman did get one little bit of correct maths in this post.

Although there is an error introduced when you add the speeds

*u* and

*v* since the object is accelerating, (in this case, a flat Earth), the speed

*w* is correct in the limit where the length of the time lapse tends to zero. And you can get an approximation by doing the calculation with a few values for the time lapse. What I found is that the convergence of this formula is very fast, so the result given here by TheEngineer (if there are no mistakes, I did not check the details) is about right.

If you check the spreadsheet I posted, you can see that Earth will approach 0.9991

*c* in less than 4 years, which means that the energy required to keep Earth accelerating was humongous even then. You can either calculate what is necessary to carry under a flat Earth to accelerate it (about three Hiroshima bombs exploding every day under every square meter of Earth's bottom, assuming perfect efficiency) or what is necessary to push Earth from its original place of creation (at least all the energy created by man to push every subatomic particle on Earth, but maybe much, much more).

Either way, pretending that Earth is moving at more than 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

*c* and that it is no deal is totally brain dead.