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

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Presentation transcript:

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

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

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

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?

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

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

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?