Which statement best describes the series ∑n=1∞1np\sum_{n=1}^{\infty} \frac{1}{n^p}∑n=1∞np1?
Converges if p>1p > 1p>1, diverges if p≤1p \leq 1p≤1
Converges if p≥1p \geq 1p≥1, diverges if p<1p < 1p<1
Converges if p>0p > 0p>0, diverges if p≤0p \leq 0p≤0
Always converges for p>0p > 0p>0