Working from the Context Panel, Maple is unable to provide a formal power series for , but it can provide one for .
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Obtain Maple's formal power series for
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Control-drag the given function.
Context Panel: Series≻Formal Power Series
Set the index to
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Use this expression to obtain the first few terms of the fulll expansion
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Control-drag the expression for the formal power series and edit , the upper limit of the sum, to say, 4.
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Context Panel: Evaluate Sum
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With an application of the appropriate command, Maple does succeed in obtaining a formal power series for the given function.
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Obtain the first few terms of the Maclaurin series for
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Control-drag the given function and press the Enter key.
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Context Panel: Series≻Series≻
The order of the series is the power in the remainder term.
To obtain an expansion containing up to terms of 4th degree, the order has to be taken as 12. To return a polynomial, and not a series data structure containing a term indicating the order of the error, check the box for "Remove order term." See Figure 8.5.9(a).
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Figure 8.5.9(a) Series dialog
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Apply the Binomial expansion from first principles
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Expression palette: Summation and binomial templates
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Apply the simplify command with the assuming option.
(Maple lost the ability to make this evaluation syntax-free.)
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Maple converts the formal expression for the Binomial series to the given function, thereby demonstrating that the Binomial series, as determined by the formula in Section 8.5, actually represents the given function.
