Math 132 Exam 2 Practice Questions Answers 1 Recall that a series is conditionally convergent if it is convergent but not absolutely For which values of p is the above series conditionally convergent cid 88 n 1 1 n np convergent A 0 p 1 B 0 p 1 C p 0 D p 1 2 Which of the following is not an improper integral A C cid 90 1 cid 90 4 0 0 1 x dx x ex 1 B x sin x dx dx D 2 x2 1 dx cid 90 cid 90 2 1 3 Which of the following series do not meet the conditions of the Integral Test I n sin n 1 cid 88 n 1 II cid 88 n 1 1 np p III cid 88 n 1 1 n n where p is a positive number A I II and III B I only C II and III D I and III 1 4 Which combination of the following properties is enough to guarantee that a sequence is convergent I an is bounded above II an is bounded below III an is decreasing IV an is increasing A I II B I III C II III D II IV 5 Which of the following are true for the Test for Divergence an does not exist then an diverges an exists but is not 0 then an diverges an 0 then an converges cid 80 n 0 cid 80 n 0 cid 80 n 0 I If lim n II If lim n III If lim n A I II B I III C I II III D II III 8n 1 2n 2 5n 8n converge or diverge If it converges what 6 Does the sequence an does it converge to Convergent to 8 7 Consider the in nite series 21 15 75 7 375 49 1875 343 Write this series in the form an Does this series converge If so nd the sum cid 88 n 1 cid 19 n 1 cid 88 n 1 cid 18 21 15 21 Convergent to 49 4 2 8 Determine whether the series is convergent or divergent Clearly state which conver 9 Determine whether the series is convergent or divergent Clearly state which conver gence test you used cid 88 n 1 nn 4 n gence test you used cid 88 n 2 3 n ln n 2 gence test you used cid 88 n 1 1 n 5n 4n 7 gence test you used cid 88 n 1 6n 5n2 4n 7 gence test you used cid 88 n 1 7n 8n 3 gence test you used cid 88 n 1 n 20n 62n 1 10 Determine whether the series is convergent or divergent Clearly state which conver 11 Determine whether the series is convergent or divergent Clearly state which conver 12 Determine whether the series is convergent or divergent Clearly state which conver 13 Determine whether the series is convergent or divergent Clearly state which conver 14 Using the Alternating Series Test we can see that converges How many terms do we need to estimate the sum with error less than 0 001 31 cid 88 n 1 1 n 1 n2 Divergent Convergent Divergent Divergent Convergent Divergent 3 15 Determine whether the series is absolutely convergent conditionally convergent or di vergent Clearly state which convergence test s you used 16 Determine whether the series is absolutely convergent conditionally convergent or cid 88 n 1 1 n n2 2n Absolutely Convergent divergent Clearly state which convergence test s you used cid 88 Conditionally Convergent 1 n 1 n2 n 2 n3 3 17 Evaluate the integral dx Convergent to 2 e 18 Evaluate the integral Divergent e x x cid 90 cid 90 1 1 0 1 1 x 2 dx 4