For the power series ∑n=1∞(−1)nxnn\sum_{n=1}^{\infty} \frac{(-1)^n x^n}{\sqrt{n}}∑n=1∞n(−1)nxn, which statement is true?
It converges absolutely at both x=1x = 1x=1 and x=−1x = -1x=−1
It diverges for all ∣x∣≤1|x| \leq 1∣x∣≤1
It converges conditionally at x=1x = 1x=1 and diverges at x=−1x = -1x=−1
It converges absolutely for all ∣x∣<1|x| < 1∣x∣<1