Tham khảo tài liệu 'advanced mathematical methods for scientists and engineers episode 2 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Hints Hint Use the Cauchy convergence criterion for series. In particular consider SN 1 SN . Hint CONTINUE Hint 1. n 2 1 n ln n Use the integral test. 2. n 2 1 ln Simplify the summand. 3. ln n 2 Simplify the summand. Use the comparison test. 4. V 1 n fo n in n in in n Use the integral test. 574 5. ln 2 In 3 1 n 1 x 7 Show that the terms in the sum do not vanish as n X 6. 0 1 ln n 20 Shift the indices. 7. 4 1 3 - 2 0 Show that the terms in the sum do not vanish as n X 8. E Log 2 0 9. This is a geometric series. V n2 - 1 n4 1 Simplify the integrand. Use the comparison test. 10. Compare to a geometric series. 2 n2 In n .
