In this section, we investigate a specific new type of series that has a variable component.

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Presentation transcript:

In this section, we investigate a specific new type of series that has a variable component.

For what values of x does the series converge? To what function does the series converge when it converges?

This is a geometric series where, and so we know where this converges and to what it converges. It converges when. It converges to.

How do we find R?

If it is a geometric series, we mimic the example from earlier. If not, we use the ratio test on

Find the interval of convergence for the given series and state to what function it converges.

Find the interval of convergence for the given series.

Show that:

Consider the power series. (a) Find the domain of f. (b) Use a partial sum to estimate f(3) within of its actual value. (c) Use a partial sum to estimate f(-3) within of its actual value.