Let f(x)=∑n=1∞xnn2f(x) = \sum_{n=1}^{\infty} \frac{x^n}{n^2}f(x)=∑n=1∞n2xn. Identify the convergence behavior at the boundary points x=1x=1x=1 and x=−1x=-1x=−1.
Converges absolutely at x=1x=1x=1, diverges at x=−1x=-1x=−1
Diverges at both x=1x=1x=1 and x=−1x=-1x=−1
Converges at both x=1x=1x=1 and x=−1x=-1x=−1
Converges at x=1x=1x=1, diverges at x=−1x=-1x=−1