Quiz 14 Solution - Math 132 Spring 2009 Quiz 14 Name_Solutions 1(1pt Version(a Give a convergent geometric series Version(b Give a convergent p series

# Quiz 14 Solution - Math 132 Spring 2009 Quiz 14...

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Math 132 - Spring , 2009 Quiz 14 Name : __ Solutions ___ 1 . (1pt) Version (a) Give a convergent geometric series. Version (b) Give a convergent p series. (a) k 0 1 2 k (b) k 0 1 k 2 2 . (1pt) Version (a) Give a divergent p -series. Version (b) Give a convergent alternating geometric series.(a)k01k(b)k01k12k3. (2pts) State fully two tests for the convergence of a series that we have covered in class.All tests are listed in the table on Page 662.4. (6pts) For each series, determine whether it converges or diverges and show your work and name the testyou use.a. Version (a)k21k1klnkIt is an alternating series. Use the Alternating Series Test (AST):(i) limk1klnk0(ii)ak11k1lnk11klnkakBy the AST, the seriesk21k1klnkconverges.Version (b)k11k12k1It is an alternating series. Use the Alternating Series Test:(i) limk12k10(ii)ak112k1112k1akBy the AST, the seriesk2