For all a > 0 and b> 1, the inequalities In (n) ≤n", n < b are true for n sufficiently large (this can be proved usingL'Hôpital's Rule).Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n > N.(Express numbers in exact form. Use symbolic notation and fractions where needed.)inequality: 11IncorrectDraw a conclusion about the convergence ofΣBecause00It is not possible to use the Direct Comparison Test to determine the convergence or divergence ofn=1(n(n))81- =1nconverges,00Σ#=1(In (n))*(In (n))also converges by the Direct Comparison Test.Because is a harmonic series, it diverges. Therefore,1100(In (n))(In (n))diverges by the Direct Comparison Test.

Given an series: ∑n=1∞1lnn8 Check if the given series is convergent or not using direct comparison…

1 (In (n)) It is not possible to use the Direct Comparison Test to determine the convergence or divergence of Draw a conclusion about the convergence of Because 21- IMBIMB 114 115 n converges, also converges by the Direct Comparison Test. (In (n)) Because is a harmonic series, it diverges. Therefore, (In (n)) (In (n)) diverges by the Direct Comparison Test.