State, by writing first four terms, the expansion of the following, where |x| < 1 (1+x)-15 - Mathematics and Statistics

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

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

Sum

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

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

= `1 - x/5 + (-1/5)(-6/5)(1/2)x^2 + (-1/5)(-6/5)(-11/5)(1/6)x^3 + ...`

= `1 - x/5 + (3x^2)/25 - (11x^3)/125 + ...`

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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 1. (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)⁻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")^(-1/4)`

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

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