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)(-(5)/4))/2*"b"^2/"a"^2 ((-(1)/4)(-(5)/4)(-(9)/4))/6*"b"^3/"a"^3 + ....]`

= `"a"^(-(1)/4)[1 + "b"/(4"a") + (5"b"^2)/(32"a"^2) + (15"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. (iv) | Page 82

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

(1 + x)⁻⁴

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 + x²)^–1

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 + 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 + 4x)^(-1/2)`

Simplify first three terms in the expansion of the following

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