Question

webwork / csu_mth 182_spring20/ hw08 / 8 HW08: Problem 8 Prev Up Next (1 pt) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge. B. A. n=1 c C. and D. G) TI en + 4 1. Does this series converge or diverge? ? n2 2. G.) Does this series converge or diverge?? 2 + 5 3. Does this series converge or diverge? 2 11 12 +4 n 5 4. Does this series converge or diverge? ? 74 +1 Note: You are allowed only three attempts on this problem. Note: In order to get credit for this problem all answers must be correct. Preview Answers Submit Answers You have attempted this problem 0 times. You have 3 attempts remaining. Email instructor

Answer 1

1. Given series be! EMS n+4 nal n2 an n+4 bna > n2 How lim an bn not lim nya n+4. n n2 - lim frow the series n=1 Hence, by limit no = = finite 1 ħ be diversent harmonic series comparison test E n=1 n2 2 nelle divergent 2. Given series be 2 Let an - 2 (22+5) , bna (²)n-1 an+5 Now lim an bn 2 lim nud 2n-1 20+5 lim 1+ S 2n-1 finite Now the series nal (²) n= be a seometric series with 101= Ž <d then by geometrie series test E Źn be conversend n=1 2 Then by limit comparison test be +5 Conversent 3. Given series bei n²+4 an n² + 4 1=1 on + nal لما let bn = hh limo nuta n2 Now lim nd) an bn n2 lim a la finite 1+ 4 n2

Now h2 be the series Conversent by P-series test. n=1 [P=2> 13 Hence, by test Boro limit comparison the series be convergent. n=1 Giren series bei n-5 n=1 n4+ +1 an nas bna Enktu 4. no now lim nad bn an lim na ant n-5 nett 5 n lim ned = 1= finite na Jrow the series series no be convergent by p-series test.[P=371) comparison test the series: Hence, by limit nos E nel be convergent. nutt

3. | A ++ the series diverse n2 the series Converse } A = { J& ฟ ฟ ซุป W the series converge 2 2 t 4 4. Te nas the series converse ทร 1441