Which of the following series CONVERGE? (Select all that apply.)
∑n=1∞ln(n)n2\sum_{n=1}^{\infty} \frac{\ln(n)}{n^2}∑n=1∞n2ln(n) (by Integral Test or Limit Comparison with 1/n21/n^21/n2)
∑n=1∞12n+n\sum_{n=1}^{\infty} \frac{1}{2^n + n}∑n=1∞2n+n1 (by Comparison with 12n\frac{1}{2^n}2n1)
∑n=2∞1n(lnn)2\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}∑n=2∞n(lnn)21 (by Integral Test or Cauchy Condensation)
∑n=1∞n!3n\sum_{n=1}^{\infty} \frac{n!}{3^n}∑n=1∞3nn! (by Ratio Test)