SAT1000 - P496

Algebra Level pending

Given that an=n2(cos2nπ3sin2nπ3) (nN+)a_n=n^2(\cos^2 \dfrac{n\pi}{3}-\sin^2 \dfrac{n\pi}{3})\ (n \in \mathbb N^+), let Sn=k=1nakS_n=\displaystyle \sum_{k=1}^{n} a_k.

bn=S3nn4n (nN+)b_n=\dfrac{S_{3n}}{n \cdot 4^n}\ (n \in \mathbb N^+), Tn=k=1nbkT_n=\displaystyle \sum_{k=1}^{n} b_k.

T10=pqT_{10} = \dfrac{p}{q}, where p,qp,q are positive coprime integers.

Submit pq+2(S100+S201+S302)\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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