Question

Infinite Series Determine the convergence or divergence of the following series by applying one of given test. Half credit will be given to those the correctly apply another test instead. n(3)"e" (Limit Comparison Test or Root Test) Identify which two series are the same and then use the Ratio Test and/or Alternat Series Test to determine if the series is convergent or divergent A. (-1)" (n-1)2-1 ns2 B. À (-1)"+1 nen c. § (-1)+1 (n + 1)2

Answer 1

n. {(3) en Q1 nal n (3) en an= there lim lango n3시 lim 174 Ingre en la - 1 lim (n/m) (3) n> or n by root nal 71 e Hence test the series ng e is divergent. The following two series Q2 Gogh (n-1) 29-1 non are equivalent. ntl S fight h22 n=1 n Now antl h 2 alim fight2 hyal Intl) ant n7N lim n nel 2 1 lim n72 2 - Ito 1 to 1 thn ( 4 <1 1 2 tene the series is by ratio test convergent.