Question

(1 point) Determine whether the following series converges or diverges. co (-1)"+1 3n5 + 6 1 Input C for convergence and D for divergence: Note: You have only one chance to enter your answer.

Answer 1

We have, nt) Z -ht n=1 the 3n5+6 This es an alternating Series . Since of the series are alternatively positive and negative. We know, An alternating series , -Uz f 43- ef Converges. 1. eaels team is numerically less than che preceding tem and. ii. lim Un NOW, We have, Un = 3.5 + 6 and anti 3.(n+1) 5+ 6 Now, Untl una 3/n+1) 5+ 46 35 + 6 - +6 4 3 n + 30 +6-23(n+1) + 6 (3.nº+6)x3-(n+1) 30% + 6 - 2 2 2 2h+ het 2+1 69 3 (n+1) + 6) [By Binomian Theorem Expansion ] nez 7 3.0 + 6
The answer sheet has three pages it is the first page
n のしろ n-1-6 nch 36 +8 - 3,6 - Pa, ? (3.25 + 6 +6) } 3.(n+1) +63 -{m, nt "gn't mean? t nagin+ o) (3.7546 ) { }(n+1) 76 [ siner, (305+6) > 0, /3 (+1²6) > (s; ? + man? + gnu Maints ) rca and rea for n 7,1 Therefore, Unt) Un pro co ée anti < un. Thes we See that the each terms of the numerically less than the Series is less than the preceding term. NOU, lim un ned lim 5 3n+ 6 nd los • 2 0 II
second page
Thus the given series fullills both the condition of convera convergence of an an alternating Serin. moto Therefore, the given series is convergent. Therefore, the answer
Third/last page