Which of these series converges by the Alternating Series Test?
∑n=1∞(−1)nnn+1\sum_{n=1}^{\infty} \frac{(-1)^n n}{n+1}∑n=1∞n+1(−1)nn
∑n=1∞(−1)n1n\sum_{n=1}^{\infty} (-1)^n \frac{1}{\sqrt{n}}∑n=1∞(−1)nn1
∑n=1∞(−1)nn!100n\sum_{n=1}^{\infty} (-1)^n \frac{n!}{100^n}∑n=1∞(−1)n100nn!
∑n=1∞(−1)ncos(n)\sum_{n=1}^{\infty} (-1)^n \cos(n)∑n=1∞(−1)ncos(n)