5. [10.08 Points] DETAILS SCALCET9 11.2.012. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find at least ten partial sums of the series. (Round your answers to ve decimal places.) y y 01.0 - CD 01.0 Q) Does it appear that the series is convergent or divergent? If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.) Z Need Help? 2. [-/0.08 Points] DETAILS SCALCET9 11.2.AE.008. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example () Show that the harmonic series is divergent. . . . Solution For this particular series it's convenient to consider the partial sums S2, 541 58: $16/ 5321 ... and show that they become large. S2 = 1+ S 4 = 1 + 2 + ( 2 + 1 ) > 1 + 2 + ( 2 + 1) -1+ Entz+(+2) +( + 8 + 7+3) > 1 + 1 + ( 1 + 1 ) + ( 2 + 2+ 2+2) 2 =1+ +1+ 1 =1+ 2 $ 16 = 1 + 2 + ( 3 + 1 ) + ( 5 + . . . + 3 ) + (8 +...+7) 2 1+1+ 1 = 1+ 2 2 2 Similarly, $32 > 1 + . $64 > 1 + , and in general szn > 1 + . This shows that Son - co as n - co and so {s,} is divergent. Therefore, the harmonic series diverges. Need Help? Read It Submit Answer6. [-10.08 Points] DETAILS SCALCET9 11.2.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER 9: Calculate the sum of the series 2 an whose partial sums are given. n=1 3\" = 7 4(o.7}" Need Help? 7. [-10.08 Points] DETAILS SCALCET9 11.2.015. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER 8n Let an = 4n+1' (a) Determine whether {an} is convergent. O convergent O divergent 0:) Determine whether i an is convergent. n = 1 O convergent O divergent Need Help? 8. [-10.08 Points] DETAILS SCALCET9 11.2.023.Ml. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Determine whether the geometric series is convergent or divergent. If it is convergent, nd the sum. (If the quantity diverges, enter DIVERGES.) 7-8+_+ 7 49 Need Help? 1. [-10.08 Points] DETAILS SCALCETQ 11.2.AE.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example 41)) Find the sum of the geometric series. 4 8 16 2++ 3 9 27 Solution The rst term is a = 2 and the common ratio is r = C] . Since |r| = C]