A Tangent Rotation Sum

★ 5/10trigonometry Recursion sequences Trigonometric Identities

Problem

A sequence $\{x_n\}$ has $x_1 = 1$ and

x_{n+1} = \frac{\sqrt{3}x_n + 1}{\sqrt{3} - x_n}.

Find $\displaystyle\sum_{n=1}^{2008} x_n$ .

Answer

Solution

Difficulty	5/10
Topics	trigonometry, Recursion, sequences, Trigonometric Identities

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