State, by writing first four terms, the expansion of the following, where |b| < |a| (a − b)−3 - Mathematics and Statistics

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

(a − b)⁻³

बेरीज

(a − b)⁻³

= `["a"(1 - "b"/"a")]^-3`

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

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

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

= `"a"^-3 [1 + (3"b")/"a" + (6"b"^2)/"a"^2 + (10"b"^3)/"a"^3 + ...]`

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Binomial Theorem for Negative Index Or Fraction

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

पाठ 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 2. (i) | 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 – 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)⁻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")^(-1/4)`

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

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