MATH 222 Test 3 Spring 2003 Name_________________

Instructions: You may use a calculator on all questions on this test. Show your work and explicitly say which convergence tests you use and include any limits you need to compute for those tests.

1. Let . Find .

2. Give an example of an increasing sequence that converges and an example of a decreasing sequence that diverges.

3. Find the fourth Taylor Polynomial about c = 1 for .

4. Find the radius and interval of convergence of the following power series:

.

5. Determine if the following series converge or diverge. Clearly state the tests you use and include any necessary limits.

a)

b)

c)

6. Does diverge, converge conditionally, or converge absolutely? Justify your answer.

7. Find the Taylor Series for f(x) = .

8. Find the sum of the series (if it converges) given by