Maharashtra State BoardHSC Science (Electronics) 11th
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State, by writing first four terms, the expansion of the following, where |b| < |a| (a + b)−4 - Mathematics and Statistics

Sum

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

(a + b)−4 

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Solution

(a + b)−4

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

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

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

= `"a"^-4 [1 - (4"b")/"a" + ((-4)(-5))/2 * "b"^2/"a"^2 + ((-4)(-5)(-6))/6 * "b"^3/"a"^3 + ...]`

= `"a"^-4 [1 - (4"b")/"a" + (10"b"^2)/"a"^2 - (20"b"^3)/"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. (ii) | Page 82
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