MATH 222 Exercises on Sequences and Series

1. Let the sequence be defined by .

a) Find the first 5 terms of the sequence.

b) Using the algebraic method from class find the limit of the sequence.

2. Use the function on the calculator to find . Identify this number.

3. Use the function on the calculator to find each of the following:

Based on the numbers you found above estimate a value of n such that is about 15.

4. Apply the integral test to .

5. Apply the Limit Comparison Test to .

6. In class we derived that . Use this result to estimate ln(3). What does x have to be to produce ln(3)?