To determine whether the series W n ya ;(_1) 3n + 1 is conditionally convergent absolutely convergent or divergent we make the following steps: 1. Check if the series is absolutely convergent. The series of absolute values 2:11 Emil: can be compared with the pseries 22:1 $ with P =:- and if the Limit Comparison Test is used then . a... _ .111: : :- Hence the series of absolute value is not convergent. so the given series is not absolutely convergent and we have to move to the next step. 2. The series is an alternating series. so we can use the AST to find ifthe series is convergent. If 6,, 2 % then lim 5,, 2:. Mao Meanwhile, the derivatlve ofthe function f(9:) = kl 1 Is : henceb" is decreasing for large n. Therefore the series is convergent by the AST. Finally we conclude that the series is conditionally convergent. Check