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# This is an example of an infinite series . PowerPoint PPT Presentation

Start with a square one unit by one unit:. 1. This is an example of an infinite series. 1. This series converges (approaches a limiting value.). Many series do not converge:. This converges to if , and diverges if. is the interval of convergence. Geometric Series:.

This is an example of an infinite series .

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#### Presentation Transcript

1

This is an example of an infinite series.

1

This series converges (approaches a limiting value.)

Many series do not converge:

This converges to if , and diverges if .

is the interval of convergence.

Geometric Series:

In a geometric series, each term is found by multiplying the preceding term by the same number, r.

Find the sum of the series, if possible.

• 5+10+20+40+…

• 1+

• 9 - 3 + 1 - +…

Diverges, no sum

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27/4

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Write an expression for the nth term.

Find the function which is represented by the given series for those x for which the series converges.

Homework

Worksheet: Geometric Series