Maharashtra State BoardHSC Science (General) 11th
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Simplify first three terms in the expansion of the following (5+4x)-12 - Mathematics and Statistics

Sum

Simplify first three terms in the expansion of the following

`(5 + 4x)^(-1/2)`

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Solution

`(5 + 4x)^(-1/2)`

= `[5(1 + 4/5x)]^(-1/2)`

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

= `5^(-1/2)[1 + (-1/2)((4x)/5) + ((-1/2)(-1/2 - 1))/(2!) ((4x)/5)^2 + ....]`

= `5^(-1/2)[1 - (2x)/5 + ((-1/2)(-3/2))/2 ((16x^2)/25) + ....]`

= `5^(-1/2) [ 1 - (2x)/5 + (6x^2)/25 + ......]`

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 3. (iv) | Page 82
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