Solution Found!
Integral Test Use the integral Test to
Chapter 10, Problem 28E(choose chapter or problem)
23-30. Integral Test Use the Integral Test to determine the convergence or divergence of the following series. Check that the conditions of the test are satisfied.
\(\sum_{k=2}^{\infty} \frac{1}{k(\ln k)^{2}}\)
Questions & Answers
QUESTION:
23-30. Integral Test Use the Integral Test to determine the convergence or divergence of the following series. Check that the conditions of the test are satisfied.
\(\sum_{k=2}^{\infty} \frac{1}{k(\ln k)^{2}}\)
ANSWER:Problem 28EIntegral Test Use the integral Test to determine the convergence or divergence of the following series. Check that the conditions of the test are satisfied. Answer ; Step-1 ; In this problem we have to determine the convergence or divergence of the given series using integral test . And also we have to check whether the conditions of the test are satisfied or not. INTEGRAL TEST DEFINITION; Suppose f is continuous , positive , decreasing function on[1, ) , and let = f(n) . Then the convergence or divergence of the series Is the same as that of the integral f(x) dx .1. If f(x) dx is convergent , then is convergent .2. If f(x) dx is divergent , then is divergent . That is bothand converge or diverge together.