Simon's copy of Binomial series for non-Natural exponent

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Simon Thomas 6 years, 1 month ago

Created this as a copy of Binomial series for non-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	2
n	integer	5
T1	integer	1
T2	rational	2/5
T3	number	-0.32

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Generated value: `integer`

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Advice

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

$(1+bx)^{n}=1+n(bx)^{1}+\frac{n(n-1)}{2!}(bx)^{2}+\frac{n(n-1)(n-2)}{3!}(bx)^{3}+...$

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

So the first three terms are

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

$(1+\var{b}x)^{\frac{1}{\var{n}}}$ = $\simplify[all,!collectNumbers]{{T1}+{T2}x+{T3}x^2}$

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This question is used in the following exam:

Binomial expansion quiz by Simon Thomas in Algebra.

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Simon's copy of Binomial series for non-Natural exponent

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Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Mathematical expression

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Error

Simon's copy of Binomial series for non-Natural exponent

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month 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`