Apply the alternating series test to determine convergence of ∑n=1∞(−1)n+1n\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{\sqrt{n}}∑n=1∞n(−1)n+1.
Converges by alternating series test because 1n\frac{1}{\sqrt{n}}n1 decreases and limn→∞1n=0\lim_{n\to\infty} \frac{1}{\sqrt{n}} = 0limn→∞n1=0
Diverges because the terms do not decrease
Converges absolutely by p-series test
Cannot be determined