Maharashtra State BoardHSC Science (General) 11th
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Answer the following: State, first four terms in the expansion of (1-2x3)-12 - Mathematics and Statistics

Sum

Answer the following:

State, first four terms in the expansion of `(1 - (2x)/3)^(-1/2)`

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Solution

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

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

= `1 + x/3 + 3/8 xx (4x^2)/9 + 15/(8 xx 6) xx (8x^3)/27 + ...`

= `1 + x/3 + x^2/6 + (5x^3)/54 + ...`

Concept: General Term in Expansion of (a + b)n
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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
Miscellaneous Exercise 4 | Q II. (18) | Page 86
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