Is the series ∑n=1∞(−1)nln(n+1)\sum_{n=1}^{\infty} \frac{(-1)^n}{\ln(n+1)}∑n=1∞ln(n+1)(−1)n convergent?
Yes, by the Alternating Series Test
No, because terms do not go to 0
Yes, it is absolutely convergent
No, it diverges by the Ratio Test