Consider the series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an where an=1nln(1+1n)a_n = \frac{1}{n} \ln(1 + \frac{1}{n})an=n1ln(1+n1). Determine its convergence.
Converges by the Limit Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21
Diverges by the Limit Comparison Test with ∑1n\sum \frac{1}{n}∑n1
Converges by the Integral Test
Diverges because limn→∞an≠0\lim_{n \to \infty} a_n \neq 0limn→∞an=0