Maharashtra State BoardHSC Science (General) 11th
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State, by writing first four terms, the expansion of the following, where |b| < |a| (a+b)14 - Mathematics and Statistics

Sum

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

`("a" + "b")^(1/4)`

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Solution

`("a" + "b")^(1/4)`

= `["a"(1 + "b"/"a")]^(1/4)`

= `"a"^(1/4) (1 + "b"/"a")^(1/4)`

= `"a"^(1/4)[1 + (1/4)("b"/"a") + ((1/4)(1/4 - 1))/(2!) ("b"/"a")^2 + ((1/4)(1/4 - 1)(1 / 4 - 2))/(3!)*("b"/"a")^3 + ...]`

= `"a"^(1/4) [1 + "b"/(4"a") + (1/4)((-3)/4)(1/2)("b"^2/"a"^2) + (1/4)((-3)/4)(-7/4)(1/6)("b"^3/"a"^3) + ...]`

= `"a"^(1/4) [1 + "b"/(4"a") - (3"b"^2)/(32"a"^2) + (7"b"^3)/(128"a"^3) + ...]`

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 2. (iii) | Page 82
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