1. For the geometric series below, what is the limit as n →∞ of the ratio of the n + 1 term to the n term?

2. For the series,
find the limit:
What does this tell you about the series?

3. For the series,
find the limit:
What does this tell you about the series?

4. The Ratio Test
For an infinite series , what does the limit
of the n + 1 term to the n term tell you about the convergence of the series?

5. For what values of x does the following power series converge?

6. For what values of x does the Maclaurin series for converge?

7. Suppose that the nth derivative a function f(x) at x = 2 is given by the formula:
What is the Taylor series for the function centered at x = 2?
What is the interval of convergence for this series?