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

Sum

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

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

#### Solution

(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 + ...

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. (iv) | Page 82