Binomial series for non-Natural exponent

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Frank Doheny

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Frank Doheny

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Ready to use

7 years ago

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Frank Doheny 7 years ago

Gave some feedback: Ready to use

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Frank Doheny 8 years, 4 months ago

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Frank Doheny 8 years, 4 months ago

Created this as a copy of Binomial series for Natural exponent.

Name	Status	Author	Last Modified
Binomial series for Natural exponent	Ready to use	Frank Doheny	20/03/2018 08:25
Binomial series for non-Natural exponent	Ready to use	Frank Doheny	20/03/2018 08:25
First 3 terms of Binomial series for Natural exponent	Ready to use	Frank Doheny	20/03/2018 08:24
Gemma's copy of Binomial series for Natural exponent	draft	Gemma Crowe	14/08/2018 15:39
Gemma's copy of First 3 terms of Binomial series for Natural exponent	draft	Gemma Crowe	14/08/2018 13:42
Algebra: binomial expansion, coefficient of particular term, calculator	Ready to use	Lovkush Agarwal	06/07/2020 11:30
Full binomial expansion	draft	Simon Thomas	27/02/2019 09:40
Simon's copy of First 3 terms of Binomial series for Natural exponent	draft	Simon Thomas	27/02/2019 10:23
Simon's copy of Binomial series for Natural exponent	draft	Simon Thomas	27/02/2019 09:44
Simon's copy of Binomial series for non-Natural exponent	draft	Simon Thomas	27/02/2019 10:24

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Question statement

Given the expression $(1+\var{b}x)^{\frac{1}{\var{n}}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	3
n	integer	2
T1	integer	1
T2	rational	3/2
T3	number	-1.125

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The binomial series expansion for an expression of the form $(1+bx)^{n}$ where $n$ is a non-natural number, is given by:

$(1+bx)^{n}=1+\tbinom{n}{1}(bx)^{1}+\tbinom{{n}}{2}(bx)^{2}+\tbinom{{n}}{3}(bx)^{3}.......$

In this example $power=\frac{1}{\var{n}}$ , and $b=\var{b}$ .

So the first three terms are

$(1+\var{b}x)^{\frac{1}{\var{n}}}=1+\tbinom{\frac{1}{\var{n}}}{1}(\var{b}x)^{1}+\tbinom{\frac{1}{\var{n}}}{2}(\var{b}x)^{2}$

$(1+\var{b}x)^{\frac{1}{\var{n}}}=\var{T1}+\var{T2}x+\var{T3}x^2$

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This question is used in the following exams:

Series quiz by Frank Doheny in Series.
P13 - Binomial Theorem by Rob Beckett in Rob's workspace.
Angharad's copy of Series quiz by Angharad Thomas in Angharad Old Stuff.
Blathnaid's copy of Series quiz by Blathnaid Sheridan in Blathnaid's workspace.
Arithmetic & Geometric Series by Michael Proudman in .Algebra.
Wenling's copy of Series quiz by Wenling Zhang in Wenling's workspace.
Series quiz short by claire lines in claire's workspace.
Series quiz long by claire lines in claire's workspace.
David's copy of Series quiz by David Elliott-Button in David's workspace.

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Frank Doheny 7 years ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 4 months ago

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Binomial series for non-Natural exponent

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`