State, by writing first four terms, the expansion of the following, where |b| < |a| (a+b)14 - Mathematics and Statistics

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" + "b")^(1/4)`

Sum

`("a" + "b")^(1/4)`

= `["a"(1 + "b"/"a")]^(1/4)`

= `"a"^(1/4) (1 + "b"/"a")^(1/4)`

= `"a"^(1/4)[1 + (1/4)("b"/"a") + ((1/4)(1/4 - 1))/(2!) ("b"/"a")^2 + ((1/4)(1/4 - 1)(1 / 4 - 2))/(3!)*("b"/"a")^3 + ...]`

= `"a"^(1/4) [1 + "b"/(4"a") + (1/4)((-3)/4)(1/2)("b"^2/"a"^2) + (1/4)((-3)/4)(-7/4)(1/6)("b"^3/"a"^3) + ...]`

= `"a"^(1/4) [1 + "b"/(4"a") - (3"b"^2)/(32"a"^2) + (7"b"^3)/(128"a"^3) + ...]`

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Binomial Theorem for Negative Index Or Fraction

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Chapter 4: Methods of Induction and Binomial Theorem - Exercise 4.4 [Page 82]

Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 2. (iii) | Page 82

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 - x)^(1/3)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 – x²)^–3

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 + x)^(-1/5)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x²)^–1

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a − b)⁻³

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a + b)⁻⁴

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" - "b")^(-1/4)`

State, by writing first four terms, the expansion of the following, where |b| < |a|

`("a" + "b")^(-1/3)`

Simplify first three terms in the expansion of the following

(1 + 2x)^–4

Simplify first three terms in the expansion of the following

`(1 + 3x)^(-1/2)`

Simplify first three terms in the expansion of the following

`(2 - 3x)^(1/3)`

Simplify first three terms in the expansion of the following

`(5 - 3x)^(-1/3)`