# 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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