2022 SSMO Relay Round 5 Problems/Problem 3

Problem

Let $T=TNYWR$ , and let $a_k=\text{cis}\left(\frac{k\pi}{T+1}\right)$ . Suppose that $\sum_{k=1}^{T+1} \frac{|a_{2k}+a_{2k+2}-a_{2k-1+T}|}{|a_{2k+1}-( a_{2k}+a_{2k+2})|}$ can be expressed in the form of $a+b\cos(\frac{\pi}{c})$ , where $\text{cis}(x) = \cos(x) + i\sin(x)$ . Find $a+b+c$ .

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2022 SSMO Relay Round 5 Problems/Problem 3

Problem

Solution