Consider the series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an where an=1n∫01/nx1+x dxa_n = \frac{1}{n} \int_0^{1/n} \frac{\sqrt{x}}{1+x} \, dxan=n1∫01/n1+xxdx. Determine its convergence status.
Converges by the Limit Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21
Converges by the Integral Test
Diverges by the p-series test
Diverges because limn→∞an≠0\lim_{n \to \infty} a_n \neq 0limn→∞an=0