How to exceed the speed of light: A tutorial

First, a bit of background. As you can learn from this article, if you stand on the front of a train and fire a gun the bullet will exit the gun at its normal speed, but will start at the speed of the train, adding those two speeds together.

Now, scientists often cite the fact that mass increases proportionally with speed to refute the concept of light-speed travel: accelerating to light speed becomes virtually impossible as whatever accelerating object becomes exponentially heavier. Additionally, said buzzkill scientists state how unrealistic the power requirements of such a speed would be. Such things considered, here is my humble proposal for intergalactic lightspeed travel.

1. Get about 10 spaceships of incrementally decreasing size, each equipped with an engine capable of propelling the first ship at 1/10 the speed of light. For the purpose of this thought experiment we are assuming technology has advanced enough to make engines that can reach this speed. Since each ship will be around a tenth smaller than its previous craft, the final ship should be capable of reaching the speed of the first ship at 10 times its weight using the same propulsion as that ship. The design of all but the last spaceship should only be complicated enough to allow it to carry the other spaceships and release its cargo on command from the front of the craft.

2. Nest all of the spaceships inside each other. The smallest spaceship should contain whatever needs to be ferried at lightspeed.

3. Launch the largest craft, carrying all the others, and bring it up its top speed (1/10th the speed of light.) 

4. Open the front of the largest craft and drive the next spaceship out, until that ship reaches its top speed. The second ship is now travelling at 2/10ths the speed of light.

5. Continue this until you have reached the 2nd to last ship. Said craft should be travelling at 9/10ths the speed of light.

6. Open the front of the last craft and fly the final ship out until it reaches its top speed. You are now travelling at the speed of light and the universe has disintegrated.