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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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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:

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

2

27/4

4



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


Homework .

Worksheet: Geometric Series


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