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Representation of Functions by Power Series
Lesson 9.9
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Geometric Power Series
Consider the function Note the similarity to the sum of the geometric series
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Geometric Power Series
Thus we could let a = 1 and r = x and have Where is this power series centered? At x = 0, for the interval -1 < x < 1 Note also that our original f(x) is defined for all x ≠ 1
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Geometric Power Series
To center this series at x = -3 you could specify Then a = ¼ r = [(x + 3)/4] So convergence would be for the interval
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Geometric Power Series
Try this out … find a power series for the function centered at c
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Operations with Power Series
Note the following rules
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Adding Two Power Series
Consider a function which can be broken into two using partial fractions Now determine two geometric power series which are added to give us a series for the original function
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Try Another Try these … just for practice See Example 4 and Example 2
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Assignment Lesson 9.9 Page 674 Exercises 5 – 25 odd
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