Find the radius of convergence \(R\) for the series \( \displaystyle \sum_{n=1}^\infty \left(\dfrac32\right)^n \dfrac n{(n+1)^2} x^n \).

Submit your answer as \( \lfloor 1000R \rfloor \). \[\]

**Bonus**: What happens to the series when \(|x| = R \) and when \(x\in \mathbb R\)?

**Notation**: \( \lfloor \cdot \rfloor \) denotes the floor function.

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