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In the following expansion, find the indicated coefficient. x–3 in (x-12x)5 - Mathematics and Statistics

Sum

In the following expansion, find the indicated coefficient.

x–3 in `(x - 1/(2x))^5`

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Solution

Let tr+1 contains x–3 in the expansion of `(x - 1/(2x))^5`.

We know that, in the expansion of (a + b)n,

tr+1 = nCr an–r br

Here a = x, b = `-1/(2x)`, n = 5

∴ tr+1 = `""^5"C"_"r" (x)^(5 - "r") (-1/(2x))^"r"`

= `""^5"C"_"r"  x^(5 - "r").(-1/2)^"r".x^(-"r")`

= `""^5"C"_"r".(-1/2)^"r".x^(5 - 2"r")`

But tr+1 contains x–3

∴ power of x = – 3

∴ 5 – 2r = – 3

∴ r = 4

∴ coefficient of x–3 = `""^5"C"_4.(-1/2)^4`

= `5 xx 1/16`

= `5/16`

Concept: Binomial Coefficients
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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 4.3 | Q 2. (iv) | Page 80
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