# Series Convergence

Calculus Level 5

$\large \sum_{n=1}^\infty \dfrac{(a-3\cos^2 n)\sin^2 n}{\sqrt n}$

Let $$a$$ be the constant value for which the series above converges.

If $$a$$ can be expressed as $$\dfrac bc$$, where $$b$$ and $$c$$ are integers, with $$b$$ positive, find $$b+c$$.

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