State, by writing first four terms, the expansion of the following, where |x| < 1 (1 – x2)–3 - Mathematics and Statistics

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

(1 – x²)^–3

योग

(1 – x²)^–3

= `1 - (- 3)x^2 + ((-3)(-3 - 1))/(2!) (x^2)^2 - ((-3)(-3 - 1)(-3 - 2))/(3!) (x^2)^3 + ...`

= `1 + 3x^2 + ((-3)(-4))/2 x^4 - ((-3)(-4)(-5))/6 x^6 + ...`

= 1 + 3x² + 6x⁴ + 10x⁶ + ...

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Binomial Theorem for Negative Index Or Fraction

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अध्याय 4: Methods of Induction and Binomial Theorem - Exercise 4.4 [पृष्ठ ८२]

अध्याय 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 1. (iii) | पृष्ठ ८२

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

Simplify first three terms in the expansion of the following

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