For the series ∑n=1∞(−1)nnn2+1\sum_{n=1}^{\infty} \frac{(-1)^n \sqrt{n}}{n^2 + 1}∑n=1∞n2+1(−1)nn, which statement is correct?
The series converges absolutely because nn2+1≤1n3/2\frac{\sqrt{n}}{n^2 + 1} \leq \frac{1}{n^{3/2}}n2+1n≤n3/21 and ∑1n3/2\sum \frac{1}{n^{3/2}}∑n3/21 converges
The series diverges because n→∞\sqrt{n} \to \inftyn→∞
The series converges conditionally but not absolutely
The series may converge by the Alternating Series Test, but diverges absolutely