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State, by writing first four terms, the expansion of the following, where |x| < 1 (1-x)-13 - Mathematics and Statistics

Sum

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

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

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Solution

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

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

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

= 1 - x/3 - x^2/9 - (5x^3)/81 - ...

Concept: Binomial Theorem for Negative Index Or Fraction
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.4 | Q 1. (ii) | Page 82
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