Determine which of the following series converge:
∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞n1 converges
∑n=1∞1n1.5\sum_{n=1}^{\infty} \frac{1}{n^{1.5}}∑n=1∞n1.51 converges
∑n=1∞1lnn\sum_{n=1}^{\infty} \frac{1}{\ln n}∑n=1∞lnn1 converges
∑n=2∞1nlnn\sum_{n=2}^{\infty} \frac{1}{n \ln n}∑n=2∞nlnn1 converges