Convergence is an issue here!

Calculus Level 4

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.

×