Maharashtra State BoardHSC Science (General) 11th
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In the following expansion, find the indicated coefficient. x9 in (1x+x2)18 - Mathematics and Statistics

Sum

In the following expansion, find the indicated coefficient.

x9 in `(1/x + x^2)^18`

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Solution

Here, a = `1/x`, b = x2, n = 18

We have, tr+1 = nCr an–r .br 

= `""^18"C"_"r"(1/x)^(18-"r") (x^2)^"r"`

= 18Cr (x–1)18–r .x2r

= 18Cr xr–18.x2r

= 18Cr x3r–18

To get the coefficient of x9, we must have

x3r–18 = x9

∴ 3r – 18 = 9

∴ 3r = 27

∴ r = 9

∴ Coefficient of x9

= `""^18"C"_9`

= `(18!)/(9!9!)`

= `(18 xx 17 xx 16 xx 15 xx 14 xx 13 xx 12 xx 11 xx 10)/(9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)`

= 48620

∴ Coefficient of x9 is 48620

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. (iii) | Page 80
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