RandolphT3W98

# RandolphT3W98 - ? Prove your answer. (c) If you estimate...

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Winter 1998 Math 21 Test #3 Name Show all your work in answering each question. 1. (6 pts each) Determine whether each sequence converges. If it does, give the value it converges to. (a) ‰± 2 3 n ² n =1 (b) 1 2 + 1 4 + ··· + 1 2 n ² n =1 (c) { n 1 /n } n =1 2. (9) Write the ﬁrst three terms of the sequence of partial sums for: X k =1 ± 1 k - 1 k +1 , , . (b) Write down an expression for the n th partial sum: (c) Does this inﬁnite series converge? If so, what does it converge to? 3. (7) Determine whether the following series converges. If so, ﬁnd the value it converges to. X n =1 3 n +1 4 n 4. (18) Consider the series X n =2 ( - 1) n - 1 n n - 1 . (a) Show that the series converges. (b) Is this series absolutely convergent or conditionally convergent
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Unformatted text preview: ? Prove your answer. (c) If you estimate the inﬁnite sum by adding together only the ﬁrst 6 terms , how good is the esti-mation? (You don’t need to calculate this approximating sum.) 5. (8) Apply the Ratio Test to determine if ∞ X n =1 n ! 2 n converges or diverges. 6. (8) Use either the Root Test or the Ratio Test to determine those values of x which make the following converge: ∞ X n =1 nx n . 7. (8 each) Determine the convergence of each. Use any method you want, but show your work . (a) ∞ X n =2 ln n n 3 (b) ∞ X n =1 n 2 3 n 2 + n (c) ∞ X n =2 1 n ln n (d) ∞ X n =2 1 n √ n 2-1...
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## This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.

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