The above series is one solution to a scenario proposed by Zeno wherein he considered a man and a turtle to race and since turtle is slower, it was given a head start of say 100m. Man being faster then sprints and makes up that 100 m. But during this time , the turtle may have covered another 10 m. So the man again has to sprint 10 m to be with turtle. But again during this time the turtle may have covered another 1 m. So does that mean the turtle wins? Because that's not practical right? The man has to eventually take over the turtle and win the race..But Everytime he tries to overcome turtle..he has to cover certain more distance..and this process will be infinite right?
The answer is we don't know..but eventually the man does take over the turtle and that's the truth. The above series is one such example wherein say the man has to initially cover 1 m and maybe during this time turtle covers 1/2 m and when man tries to cover these 1/2 m , the turtle may have covered 1/4 m and this goes on. So to prove that man always wins I took this example and proved that the man has to actually run 2m so to overcome the turtle. But the thing is this is an infinite process. And if I assume that each step takes minimal amount of time let's say for example each step takes 1 sec this means the man has to run for 2 m and he will surely win.
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