(b) Use the alternating test to study the convergence of the series x 2" Σ(-1)" n! n=1 Remember to justify all the hypothesis needed to use the test in both parts of this exercise.
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- Study the series about its convergence.2 6. Consider 2n=4 n2-3n a) Explain why convergence of this series cannot be proven by the Direct Comparison Test. b) Identify two convergence tests that could be used instead. Do not conduct the tests.c)Test the series 2n =0 3n+1 for convergence or divergence.(write C or D) Answer:
- Test the convergence of En=2 (-2)+3"(n+1) n251+n by ratio test.5. Use an appropriate test to determine the convergence or divergence of each series. Identify the test used. (a) 5 3n²+1 (b) 5(-)" 5n2+3 n=1 n=1 (c) E n2 Vn n=1 (d) Ž 2n n=1 (f) I 6"+n² 6n+n4 n=1 (e) -2n e n=0 (8) Č 3" 3+7n n=0 (h) Č Vn 9n2+4 n=1 n=24. Which of the following series converge and which diverge? Explain your answers: Explain your opera- tions using the appropriate CONVERGENCE test (Ratio Test or Root Test) (a) (-2)" 3" (6) E()" Зп - 1 n=1 3n n=1