N 1 cos n π ln 3 n 4 n 1 48 n 7 2 n answers

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3. n = 1 cos ( n π ) ln ( 3 n ) 4. n = 1 ( 48 ) n 7 2 n
C D A (correct)
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6. (1 point) Determine whether the series is absolutely con- vergent, conditionally convergent, or divergent: n = 1 cos ( n π / 3 ) n ! Input A for absolutely convergent, C for conditionally conver- gent, and D for divergent: Answer(s) submitted: A (correct) 7. (1 point) Determine whether the following series is abso- lutely convergent, conditionally convergent, or divergent. n = 1 ( - 1 ) n - 1 n n A (correct) 10. (1 point) Consider the series s = n = 2 a n = n = 2 n 2 + 5 5 n . (a) Find the ratio of successive terms. Express the answer as a fully simplified fraction. For n 2 : a n + 1 a n = (b) Using the result in part (a), evaluate the following limit. lim n a n + 1 a n = Note: If necessary, enter infinity for and DNE for ”does not exist”. Answer: Note: Enter A if it is absolutely convergent, C if it is con- ditionally convergent, and D if it diverges. Answer(s) submitted: A (correct) 8. (1 point) Determine whether the series is absolutely con- Answer(s) submitted: A (correct) 10. (1 point) Consider the series s = n = 2 a n = n = 2 n 2 + 5 5 n . (a) Find the ratio of successive terms. Express the answer as a fully simplified fraction. For n 2 : a n + 1 a n = (b) Using the result in part (a), evaluate the following limit. lim n a n + 1 a n = Note: If necessary, enter infinity for and DNE for ”does not exist”.
vergent, conditionally convergent, or divergent: n = 1 ( - 8 ) n n 2 Input A for absolutely convergent, C for conditionally conver- gent, and D for divergent: Answer(s) submitted: D (correct) 9. (1 point) Determine whether the series is absolutely con- vergent, conditionally convergent, or divergent: n = 1 n ( - 2 ) n 9 n Input A for absolutely convergent, C for conditionally con- vergent, and D for divergent: