Consider the alternating series ∑n=1∞(−1)nnn+2\sum_{n=1}^{\infty} \frac{(-1)^n \sqrt{n}}{n + 2}∑n=1∞n+2(−1)nn. Which statement is correct?
The series converges absolutely
The series converges conditionally because the alternating series test applies but absolute convergence fails
The series diverges
The series converges absolutely by the p-series test