Calculate

Exam 4 Name___________________________________ This is a take home exam. Rules: open book/notes, not open neighborhood. You must turn in your own work. Grading: must show all work and the final answer must be correct to receive a credit. No partial points. Good luck!

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the Divergence Test to determine whether the series diverges or state that the test is inconclusive.

1) k=2

k ln30 k

1)

Use the integral test to determine whether the series converges.

2) n=1

cos 1/n n2

2)

1

3) n=1

3n n2 + 3

3)

Determine the convergence or divergence of the series.

4) k=1

1 5

k20 4)

2

Use the ratio or root test test to determine if the series converges or diverges.

5) n=1

n! e-4n 5)

6) n=1

(2n)! 7n n!

6)

3

7) n=1

nn

2n 2

7)

8) n=1

(n!)4n

(4n)! n 8)

4

Use the Comparison Test to determine if the series converges or diverges.

9) n=1

2 + 9 cos n n3

9)

Use the limit comparison test to determine if the series converges or diverges.

10) n=1

8 n 4n3/2 - 9n + 7

10)

5

Determine convergence or divergence of the series.

11) n=1

5n2 + 6 n4 + 7n + 6

11)

Determine convergence or divergence of the alternating series.

12) n=1

(-1)n

7n3 + 5 12)

6

13) n=1

(-1)n ln 5n + 6 4n + 5

13)

Determine if the series converges absolutely, converges, or diverges.

14) n=1

(-1)n (n!)22n (2n + 1)!

14)

7

15) n=1

(-1)n 1 3

- 8 n

n 15)

Find the series' interval of convergence and radius of convergence.

16) n = 0

(x - 3)n 9n + 5

16)

8

17) n=0

(x - 9)n

n42n 17)

Use ex = k=0

xk k!

, for < x < , to find the power series representation for the given function.

18) f(x) = e9x 18)

9

Use the geometric series f(x) = 1

1 - x =

k=0 xk , for x < 1, to find the power series representation for the given function

(centered at 0).

19) f(x8) = 1

1 - x8 19)

10