Gemma's copy of First 3 terms of Binomial series for Natural exponent

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Gemma Crowe 6 years, 8 months ago

Created this as a copy of First 3 terms 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 $(\var{a}+\var{b}x)^{\var{n}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	9
n	integer	5
c	number	116640
k	integer	3

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Generated value: `integer`

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"Unnamed part" - Correct answer

Advice

The binomial series expansion for an expression of the form $(a+bx)^n$ where $n$ is a Natural number is given by:

$(a+bx)^n=\tbinom{n}{0}(a)^n(bx)^{0}+\tbinom{n}{1}(a)^{n-1}(bx)^{1}+\tbinom{n}{2}(a)^{n-2}(bx)^{2}+...\tbinom{n}{k}(a)^{n-k}(bx)^{k}+...\tbinom{n}{n}(a)^{0}(bx)^{n}$

In this example $n=\var{n}$ , $k=\var{k}$ , $a=\var{a}$ and $b=\var{b}$ .

So the first three terms of the binomial series expansion are:

$\var{a}^{\var{n}}+\tbinom{\var{n}}{\var{1}}*\var{a}^{\var{n}-1}*\var{b}^{1}+\tbinom{\var{n}}{2}*\var{a}^{\var{n}-2}*\var{b}^{2}$

$=\simplify{{a}^{n}}+\simplify{{n}*{a}^({n}-1)*{b}}x+\simplify{{n}*{n-1}*{a}^{{n}-2}*{b}^2/2x^2}$

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Gemma's copy of First 3 terms of Binomial series for Natural exponent

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Taxonomy: mathcentre

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Gemma Crowe 6 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Mathematical expression

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Gemma's copy of First 3 terms of Binomial series for Natural exponent

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Gemma Crowe 6 years, 8 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`