Determine the convergence of ∑n=3∞1n(lnn)2(lnlnn)\sum_{n=3}^{\infty} \frac{1}{n(\ln n)^2 (\ln \ln n)}∑n=3∞n(lnn)2(lnlnn)1. Which statement is correct?
Integral Test shows the integral diverges; series diverges
By Bertrand's Theorem with p=2>1p=2 > 1p=2>1; series converges
Limit Comparison to 1nlnn\frac{1}{n \ln n}nlnn1 shows divergence
Direct Comparison to harmonic series; series diverges