Question

(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) 1. n=1 (ln(n))51 n+ 5 cosé(n)vn n3 2.Σ n=1 2n3 3. 4. n8 + 10 cos(n)vn 2n + 10 6n8 – n4 +2vn 2n10 – – n3 +5 n=1 TT n=1

Answer 1

Converges by p-series test, then by comparison, Solution Let E an= TM8 (Inchis nal nis. an= (lnings An 45. < Anons his N73 nes we have diverges, then by comparistion nts test 8 W I a (Oninis nts nal Converg diverges (2) Let Costin) in nal nal n3 Cas²(n). Un an= 1.5 13 3 YOU E n 5/2 test cos² (n). Un 2 ha converges, n3 3) Let E an 23 n=1 8 WT E nal ne +10 an= an an3 not 10 no (+ 10 2 h5/14 10 Let br= - & lim an q ns an too bn line no nellt 10 ho) no an I lim nto 2 (strite) 2 (tol 0,32 6

Converges then by. 1 na no limit comparision test. an3 na converges, no +10. let ų ana Cosh). ſh nal SWT an+ 10. an= Cos(n) un ant 10 We can not apply cepply. Comparision limit comparison test. this serill. test & het { an= nal 쁜 and nt. +255 h4 anto - n25. erils. converges. by limit comparision test.