This is no ordinary Fibonacci spiral

Calculus Level 5

There is a race being held in the city of Mathville, the capital city of Mathematica. The race commences at the city centre. The competitors must first run 1 hectometre east, then 1 hectometre north, then \(\dfrac{1}{2}\) hectometres west, then \(\dfrac{1}{3}\) hectometres south, \(\dfrac{1}{5}\) hectometres east and so forth where the nth side of this spiral is \(\frac{1}{F_n}\) hectometers (\(F_n\) denotes the nth Fibonacci number). Assuming the race goes on infinitely, the distance displaced by the competitors can be represented as \(l\) metres. Find \(\lfloor {l} \rfloor\).

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