Question

(1 point) For each of the following series, tell whether or not you can apply the 3-condition test (.e. the alternating series test). If you can apply this tost, enter the series diverges, or if the series converges. If you can't apply this test (even if you know how the series behaves by some other test), enter N. 1. 3 (-1) 2 Σ (-1) n! (-1'n! 3. (-1) cos() 5. (-1) 2 + 5 6. (-1)

Answer 1

o (-1)hn! Mo Mo n=1 en by the the 3-condition test (6) by the 3-cond. test (CD) (-17hnn n=1 n! Caighn! nn Š co (1) cos(no) by the 3-condh the 3-cond. test (c) 4 by the 3- conder test (N) hel ns 5 by the 3- Cond. test (N) Ft n²+5 (-1) en n! by the 3-cond. test (c) h-

Answer 2

Alternating series test does not prove divergence; if the first condition of alternating series test is not met then by divergence term test, the series would be divergent. So in this question, D is not an answer.