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This Demonstration shows graphically and numerically the quality of approximating the function values of

for any

by the Taylor polynomial

, where

Contributed by: Reinhard Simonovits
With additional contributions by: Bernd Thaller

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Review questions:

Let

and

. How large is the error?

Let

. For what

is the error less than 0.01?

Let

and

. How large is the error?

Let

. Check the error for

. (The point

is the "best" point since it is the expansion point.)

For

, at which

is the error largest?

For

and

, how large is the error?

For

and

, how large is the error?

Geometric Series (Wolfram MathWorld)

Reinhard Simonovits

"Quality of Approximation by Geometric Series"
http://demonstrations.wolfram.com/QualityOfApproximationByGeometricSeries/
Wolfram Demonstrations Project
Published: September 13, 2012

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Quality of Approximation by Geometric Series

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