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Unformatted text preview: 4. (20 pts.) Series II: For each of the following, tell whether the given series converges absolutely, converges conditionally, or diverges. If it converges, approximate its value, explain how you approximated its value and give an estimate of the error in your approximation. (Remember to explain how you know whether the series converges or diverges.) (a) X n =1 5 2 n 3 + 1 (b) X n =5 (1) n 1 n + 3 5. (20 pts.) Proofs: Prove the following: (a) X n =1 1 (3 n2)(3 n + 1) = 1 3 (b) The series X n =1 (1) n +1 2 n + 1 converges conditionally. The number of terms required to approximate its value to within 1012 is at least 5(10 11 )....
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 Winter '98
 MathDep
 Calculus

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