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Unformatted text preview: Mat104 Fall 2002, Infinite Series Problems From Old Exams For the following series, state whether they are convergent or divergent, and give your reasons. (1) 1 n , diverges by the limit comparison test (LCT) (2) converges by ratio test (3) converges by ratio test (4) 1 n , diverges by LCT (5) 2 n 3 n , converges by LCT (6) converges by the alternating series test (AST). It is conditionally convergent only since taking absolute values gives a divergent sum. (ln n < n implies that ln(ln n ) < ln n so 1 ln(ln n ) > 1 ln n > 1 n ) (7) converges by AST, conditionally convergent since summing 1 / n gives a divergent series (p-test with p = 1/2). (8) convergent by LCT (9) 1 n 3 so convergent by LCT (10) diverges since a n as n . (11) 1 n so divergent by LCT (12) convergent by the ratio test (13) conditionally convergent (14) converges by ratio test. a n +1 /a n 1 /e ....
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- Fall '07
- Infinite Series