How do you know if the series #((-1)^n)*sqrt(n)/(ln(n))# converges or diverges for (n=2, ∞) ? Calculus Tests of Convergence / Divergence Direct Comparison Test for Convergence of an Infinite Series 1 Answer Cesareo R. May 30, 2016 The series is divergent Explanation: #sqrt k > log(k)# for #k = 2,3,4,...# Answer link Related questions What is the Direct Comparison Test for Convergence of an Infinite Series? How do you use the direct comparison test for infinite series? How do you use the direct comparison test for improper integrals? How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo5/(2n^2+4n+3)# ? How do you use the direct Comparison test on the infinite series #sum_(n=1)^ooln(n)/n# ? How do you use the direct Comparison test on the infinite series #sum_(n=2)^oon^3/(n^4-1)# ? How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo9^n/(3+10^n)# ? How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo(1+sin(n))/(5^n)# ? How do you use the direct Comparison test on the infinite series #sum_(n=1)^ooarctan(n)/(n^1.2)# ? How do you use basic comparison test to determine whether the given series converges or diverges... See all questions in Direct Comparison Test for Convergence of an Infinite Series Impact of this question 6543 views around the world You can reuse this answer Creative Commons License