Which of these series is convergent?
∑n=2∞1nlnn\sum_{n=2}^{\infty} \frac{1}{n \ln n}∑n=2∞nlnn1
∑n=2∞1n2lnn\sum_{n=2}^{\infty} \frac{1}{n^2 \ln n}∑n=2∞n2lnn1
∑n=1∞sin(1/n)\sum_{n=1}^{\infty} \sin(1/n)∑n=1∞sin(1/n)
∑n=1∞nsin(1/n2)\sum_{n=1}^{\infty} n \sin(1/n^2)∑n=1∞nsin(1/n2)