Analyze the convergence of ∑n=2∞1np(lnn)q\sum_{n=2}^{\infty} \frac{1}{n^p(\ln n)^q}∑n=2∞np(lnn)q1. For p=1p=1p=1, which range of qqq ensures convergence?
q>1q > 1q>1
q≥1q \geq 1q≥1
q<1q < 1q<1
q>0q > 0q>0