For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this can be proved using L'Hôpital's Rule). Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n 2 N. (Express numbers in exact form. Use symbolic notation and fractions where needed.) inequality: 11 Incorrect Draw a conclusion about the convergence of Σ K Because 00 It is not possible to use the Direct Comparison Test to determine the convergence or divergence of n=1 (n(n))8 1- =1 n converges, 00 Σ #=1 (In (n))* (In (n)) also converges by the Direct Comparison Test. Because is a harmonic series, it diverges. Therefore, 11 =) 00 (In (n))* (In (n)) diverges by the Direct Comparison Test.
For all a > 0 and b> 1, the inequalities In (n) ≤n, n < b are true for n sufficiently large (this can be proved using L'Hôpital's Rule). Let N be this sufficiently large n. Write an inequality comparing (In (n)) and n for n 2 N. (Express numbers in exact form. Use symbolic notation and fractions where needed.) inequality: 11 Incorrect Draw a conclusion about the convergence of Σ K Because 00 It is not possible to use the Direct Comparison Test to determine the convergence or divergence of n=1 (n(n))8 1- =1 n converges, 00 Σ #=1 (In (n))* (In (n)) also converges by the Direct Comparison Test. Because is a harmonic series, it diverges. Therefore, 11 =) 00 (In (n))* (In (n)) diverges by the Direct Comparison Test.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.8: Solving Absolute Value Equations And Inequalities
Problem 3E
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