Fish with binary speed

There are \(n\) fish numbered \(1\) through \(n\) at one end of an aquarium. They all start swimming at the same time to the other end of the aquarium. Once a fish reaches an end of the aquarium, it turns around immediately and continues swimming in the other direction.

Fish \(1\) swims with speed \(v_1\), fish \(2\) swims with speed \(v_2 = 2 v_1\), fish \(3\) swims with speed \( v_3 = 2 v_2 \), and so on.

Will the \(n\) fish all be at the same end of the aquarium at the same time again?

An example aquarium with \(n=3\) fish.

An example aquarium with \(n=3\) fish.

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