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Unformatted text preview: From the files of Norman Dobson (edited by T. Gideon) Calculus II – Final Exam Problems Sequences, Geometric and Telescoping Series 1. Given the sequence 1 + ln n n 3 ∞ n =1 (a) Is it monotonic? Is it bounded? (b) What can be concluded from (a)? 2. Illustrate each of the following with an exam- ple. (a) A bounded sequence need not converge. (b) A monotonic sequence need not be bounded. 3. If possible, state an example for each of the following (a) A convergent sequence which is not mono- tonic. (b) A convergent sequence which is not bounded. 4. Determine whether each sequence is conver- gent or divergent? If convergent find what it converges to. If divergent, state when it di- verges to ∞ or-∞ . (a) n √ n +1 n o ∞ n =1 (b) n n 2 n ! o ∞ n =0 (c) n n !2 n (2 n )! o ∞ n =0 (d) a n =- 2 + ln h 2+ n 3 n i , n = 1 , 2 , 3 ,... (e) a n = (5 n ) 3 / ln n , n = 2 , 3 , 4 ,... (f) n 2 n +1 3 n- 1 o ∞ n =1 (g) a n = ln(2 n + 1)- ln n, n = 1 , 2 , 3 ,......
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- Spring '08
- Calculus, n=1, sum converges, Norman Dobson, T. Gideon