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On exercises 5-8, show whether the series converges or diverges using an appropriate test. * 2k+33k-3 5) k* in n + 3n-2 n²+1* 2k+Ik! (k+3) 7)

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Answer #1

Sol : given that K-3 K+3 3 S 2 k=3 kБ given let ak = **! 3KS kk (k+1) 73 · K+1-3 Akti - 3 (katt/ K-2 3 K+4 AKAL = 2 . Ratio t(-) n3 +3n-2 kol n²tt Now by the Alternative test if by to © im by → @ {by J is seasing then Žan ý Sequene is converget othe- Kad ak ked ak Hele ak = ett kb (K3)! By the ratio test akti= mekt°q640! (k+d)! By use of deft lim akti. .(+! x (+3)! (K-14)hot hot ( It onto) - 2 9 712 12 Now by the compessim test bn = nu ma i by ptest , pol Convergent Pel is divergent Hele z bna

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