Question

2. Use the limit comparison test to determine whether the following series converge or diverge. n Α.Σ 2 + n3 n=2 2n3 - n B. S 3n5 + 2n2 + 1 n=1 5" c. S 3" + 2 n= In(n) 1 D. Σ (Hint: Try comparing this to n2 n3/2 n=3 n=3 I MIMO Ε.Σ sin (1) (Hint: Try comparing this to n n=1 n=1

Answer 1

Solution 4) Here n 1 Gд. — Let un n 2th3 n3 (142/n) 62 (142/6) series 4 is convergent by p-series test for p=2>1 lim n² and t h-> Un که جا 1+2143 ito - senes un is also also convergent by limit comparision test B) an²h un n3 (2-1,2) 3n+2n²+1 no (3+2/23 + 4/95) ( 2-1/12) (3+2/13 4 1/ns) a series {vn is convergent by posetes test for p = 221 h2 N h CS let Scanned with CamScanner

2-0 دوره -2 2 hugou 3toto and lim un lim (2- 1/12) hoorn (3 + 2/63+ '/h) y series Ehing is also convergent by (out comparisien test 11 c) sh 3+2 Here un then lim Unti tus will et HUE cotu sh 3h+2 no un lim s(lto) SA Unti 5 (477 i lim hoo nyo un 3(10) 3 3( 1+ 2/38+) series su is divergent by is divergent by Ratio test. Since. ६८प व h3/2 In²in) h2 convergent by p-series test for p =321 touts pun IN is con 13/2 Serige In 2(6) ha is also convergent by comparision test. LA Since Sin(n) L TEMA 14 pub series convergent by posesies test for p=27 h2 Sch(n) is also convergent by comparisjon testo Tos Panaderies n CamScanner