Achilles and the tortoise/Series/Exercise

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The situation in the turtle paradox of Zenon of Elea is the following: a slow turtle (with speed ) has a starting point compared with the faster Achilles (with speed and starting point ). They start at the same time. Achilles can not catch the tortoise: when he arrives at the starting point of the tortoise , the turtle is not there any more, but a little further, let's say at the point . When Achilles arrives at the point , the turtle is once again a bit further at the point ,

and so on. Calculate the elements of the sequence , the associated time points , and the respective limits. Compare these limits with the distance point where Achilles catches the turtle (you can calculate it directly from the given data).