# SAT1000 - P496

Algebra Level pending

Given that $a_n=n^2(\cos^2 \dfrac{n\pi}{3}-\sin^2 \dfrac{n\pi}{3})\ (n \in \mathbb N^+)$, let $S_n=\displaystyle \sum_{k=1}^{n} a_k$.

$b_n=\dfrac{S_{3n}}{n \cdot 4^n}\ (n \in \mathbb N^+)$, $T_n=\displaystyle \sum_{k=1}^{n} b_k$.

$T_{10} = \dfrac{p}{q}$, where $p,q$ are positive coprime integers.

Submit $\lfloor p-q+2(S_{100}+S_{201}+S_{302}) \rfloor$.

Have a look at my problem set: SAT 1000 problems

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