Which test would you apply to determine convergence of ∑n=2∞1n(lnn)(lnlnn)2\sum_{n=2}^{\infty} \frac{1}{n(\ln n)(\ln \ln n)^2}∑n=2∞n(lnn)(lnlnn)21?
Integral Test; the series converges
Cauchy Condensation Test; ∑2n⋅12n(nln2)(ln(nln2))2\sum 2^n \cdot \frac{1}{2^n(n\ln 2)(\ln(n\ln 2))^2}∑2n⋅2n(nln2)(ln(nln2))21 converges
Limit Comparison Test with 1n2\frac{1}{n^2}n21; the series converges
Divergence Test; the terms approach 0, so the series diverges