I don't know how do you derive that and what is n stand forProbably you have misunderstanding in my question.
Apparently, as long as worm speed > 0, the speed of worm relative to ground is increasing at every time instance and approaching the string stretching speed. Since the increasing of worm speed will never stop until reaching string stretching speed, it will definitely catch up after some time.
while. we need formula to prove that. think e.g the worm speed is a function
that converge to certain limit, as series 1+1/2+1/6+1/12, it increase but converge at some level.
my n is the time, in a discrete way.
my n is the time, in a discrete way.
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