# 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 \(b+c\).