# Walking on logs

Calculus Level 5

A man begins his journey at the origin $$(0,0)$$ of the Cartesian plane. He then walks $$\ln\left(\frac{8}{4}\right)$$ units right (positive $$x$$ direction), $$\ln\left(\frac{9}{5}\right)$$ units up (positive y direction), $$\ln\left(\frac{10}{6}\right)$$ units left (negative $$x$$ direction), $$\ln\left(\frac{11}{7}\right)$$ units down (negative $$y$$ direction).

He continues this pattern indefinitely with the $$n$$-th side of this spiral being of length $$\ln\left(\frac{n+7}{n+3}\right)$$ starting with $$n=1$$.

Find the positive distance (magnitude) that the man will travel from the origin. Give your answer to 2 decimal places.

Inspired by my classmate Kaishu Mason

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