Determine the convergence of ∑n=3∞1nlnn\sum_{n=3}^{\infty} \frac{1}{n \ln n}∑n=3∞nlnn1 using the Integral Test.
Converges; ∫3∞dxxlnx\int_3^\infty \frac{dx}{x \ln x}∫3∞xlnxdx converges
Diverges; ∫3∞dxxlnx=∞\int_3^\infty \frac{dx}{x \ln x} = \infty∫3∞xlnxdx=∞
Converges; ∫3∞dxxlnx\int_3^\infty \frac{dx}{x \ln x}∫3∞xlnxdx is bounded
The Integral Test does not apply to this series