Does the power series ∑n=1∞(−1)nxnn\sum_{n=1}^{\infty} \frac{(-1)^n x^n}{n}∑n=1∞n(−1)nxn converge at x=1x = 1x=1?
Yes, by the Alternating Series Test
No, because limn→∞1n≠0\lim_{n \to \infty} \frac{1}{n} \neq 0limn→∞n1=0
Yes, by the Ratio Test
No, the series diverges everywhere