Start with a square one unit by one unit:
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This is an example of an infinite series . PowerPoint PPT Presentation


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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:.

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This is an example of an infinite series

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 is an example of an infinite series

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.


This is an example of an infinite series

Find the sum of the series, if possible.

  • 5+10+20+40+…

  • 1+

  • 9 - 3 + 1 - +…

Diverges, no sum

2

27/4

4


This is an example of an infinite series

Write an expression for the nth term.


This is an example of an infinite series

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


This is an example of an infinite series

Homework

Worksheet: Geometric Series


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