If lim = 0 and 2=1 _ converges, then Zk=1 . parison test (converges/diverges). e terms are 16. If lim uk = 0 and koo bk Ck=1 ak converges, explain why we cannot draw any conclusions about the behavior of comparison ries whose r statement 17. Fill in the blanks and select the correct word: If lim "k = co and _k=1 _ diverges, then Ek=1 xplain why (converges/diverges). divergent 18. If lim "k = 0% and Cak diverges, explain why we limit com- cannot draw any conclusions about the behavior of es, explain a conver- 19. In Example 1 we used the comparison test to show that r the limit Too *312 - k - 1 the series _k=1 5/3 + 3 converges. Use the limit com- parison test to prove the same result. ntages of behavior 20. In Example 1 of Section 7.4 we used the integral test to show that the series _=1 -2 converges. Use the limit comparison test with the series _ke1 x to prove the same result. sts to de- 00 1 + Ink 8 1 Explain 27. 28. K2 K= 1 ( k - IT ) 2 test you k=1 1 + Ink sin k 2 29. 30. K 3 K=1 k =1 k englov Use any convergence test from this section or the previous sec- tion to determine whether the series in Exercises 31-48 con- verge or diverge. Explain how the series meets the hypotheses of the test you select. 00 31. K-1/2 Hiwe eat 32. K-4/3 k =1 K = 1