Evaluate the convergence of ∑n=1∞1nln(1+1np)\sum_{n=1}^{\infty} \frac{1}{n} \ln\left( 1 + \frac{1}{n^p} \right)∑n=1∞n1ln(1+np1) for p>0p > 0p>0.
Converges for all p>0p > 0p>0.
Converges if p>1p > 1p>1, diverges if 0<p≤10 < p \leq 10<p≤1.
Converges if p>0p > 0p>0, diverges if p≤0p \leq 0p≤0.
Always diverges.