Can you help me with the following two problems. For the first, one you can use any method of convergence or divergence and I have a feeling it is the integral test. Thanks so much! :)

\f33. Show that - 2 + 3 - 3 converges by computing the partial sums. Does it converge absolutely? 34. The Alternating Series Test cannot be applied to 1 + 2 2 32 + 23 33 it... NI 3 Why not? Show that it converges by another method. 35. Assumptions Matter Show that the following series diverges: + ... NI - 4 00 1 16 (Note: This demonstrates that in the Alternating Series Test, we need the assumption that the sequence an is decreasing. It is not enough to assume only that 'an tends to zero.) ms Sn 36. Determine whether the following series converges conditionally: below 1 1 3 2 5 + + 11 t ... series of SN. 37. Prove that if _ an converges absolutely, then a? also converges. diverges. Give an example where > an is only conditionally convergent and Can endilast n ) is a 39. Use Exercise 38 to show that the following series converges: In 2 2 In 3 In 4 + In 5 In 6 2 In 7 + ... 2, and 40. Prove the conditional convergence of 1+ w