Question

Determine whether the given series is absolutely convergent, conditionally convergent, or divergent. Support your conclusion with a well-written argument that names any series test used, shows the conditions of the series test(s) utilized are met, provides calculation(s) to show a conclusion can be made, and summarizes your findings at the end. (a) In=1(-1)"sin () (-1)" (n-2) (C) 2n=1 ºnin (c) En=1 (e) En=4 (-1)", (b) 20 (-1)" (n2+n+ 2) (0) 2n=1 n42) (d) =2 (–1)M (1+2)" (1) =1 (–1)n+1 2012 4+ 2n+ 3 4) Consider the series En a) Show the series is convergent and determine the type of convergence. Be sure to provide a careful argument to prove the type of convergence and name any series tests you apply. b) What is the smallest integer N so that SN approximates the sum of the series accurate to less than 10-4? What is this approximation? c) Is the approximation given in part (b) an overestimate or an underestimate? Explain.

Answer 1

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Explanation:

in summarizing the findings at the end. with (a) In=1(-1)"sin () (-1)" (n-2) (C) 2n=1 ºnin (c) En=1 (e) En=4 (-1)", (b) 20 (-1)" (n2+n+ 2) (0) 2n=1 n42) (d) =2 (–1)M (1+2)" (1) =1 (–1)n+1 2012 4+ 2n+ 3 4) Consider the series En

As well as to calculate the smallest integer, The negative integers will go on with no bound and getting lesser and lesser for ever.

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