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Math 133 HW 9: due Tuesday, November 14 in class Be sure to show your work! Decide whether each of the following infinite series is absolutely convergent (A.C.), conditionally convergent (C.C.), or divergent. If you use a series test, indicate which test you’re using and explain why the hypotheses hold. 1. ∞ X (−3)n n2 n=1 2. ∞ X (−1)n−1 n=1 3. ∞ X (−1)n+1 (2n)! ∞ X (−1)n n(2n) ∞ X 6. ∞ X The series converges absolutely e(n2 ) √ n=1 The series diverges (n!)2 n=1 5. The series converges conditionally 3 + 5n n=1 4. The series converges absolutely 22n (−1)n n2 + n + 1 The series converges conditionally √ n (−1) n=1 n n3 + 2 ∞ X (−2)n 7. n + 5n The series converges absolutely The series converges absolutely n=1 8. ∞ X (−1)n · √ n 10 The series diverges n=1 9. ∞ X n sin(n) n=1 10. n3 The series converges absolutely 2 ∞ X (−1)n n100 100n n=1 n! The series converges absolutely 1
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