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)-13 - Mathematics and Statistics

Sum

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

`("a" + "b")^(-1/3)`

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Solution

`("a" + "b")^(-1/3) = ["a"(1 + "b"/"a")]^(-1/3)`

= `"a"^(-1/3)(1 + "b"/"a")^(-1/3)`

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

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

= `"a"^(-1/3) [1 - "b"/(3"a") + (2"b"^2)/(9"a"^2) - (14"b"^3)/(81"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. (v) | Page 82
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