A Series of Curving Lines

Imagine line segment AB flat on a horizontal axis with a length of 1. Line segment BC with a length of 1/2 connects to it forming angle ∠ABC with a measure of 179°. Then line segment CD connects, has a length of 1/3 , forms angle ∠BCD with 178° angle. Then line segment DE connects, has a length of 1/4 , forms angle ∠CDE with 177° angle. And so on, until it ends on a line segment forming an angle with a measure of 1°.

At which line segment will this series of line segments extend to the opposite side?

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$