Worms and divergent series
 
|
Imagine a worm at one end of a rubber rope. The rope is 1 km long and the worm crawls along the rope at a steady pace of, say, 1 cm per second. |
|
Just after the first second the rope stretches to 2 kilometers, like a rubber band, while the worm goes on at the same pace of 1 cm per second. |
|
After the next second the rope stretches to 3 kilometers, and so on. The worm goes on its way, always at the same speed. |
Now the question is: Will the worm ever reach the end of the rope?
Try to answer the question observing that the rope stretches uniformly, like a rubber band, so that at the end of the first second also the distance already covered by the worm stretches.
If this problem is beyond you, you can see the solution.