Maharashtra State BoardHSC Science (Electronics) 11th
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Find the constant term (term independent of x) in the expansion of (x-2x2)15 - Mathematics and Statistics

Sum

Find the constant term (term independent of x) in the expansion of `(x - 2/x^2)^15`

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Solution

Here, a = x, b = `(-2)/x^2`, n = 15

We have, tr+1 = nCr an–r .br 

= `""^15"C"_"r" (x)^(15 - "r")*((-2)/x^2)^"r"`

= 15Cr x15–r.(–2)r. x–2r

= 15Cr (–2)r x15–3r

To get the term independent of x, we must have

x15–3r = x0

∴ 15 – 3r = 0

∴ r = 5

∴ the term independent of x

= 15C5 (– 2)5

= `(15!)/(5!10!)(-2)^5`

= `(15 xx 14 xx 13 xx 12 xx 11)/(5 xx 4 xx 3 xx 2 xx 1) xx (-32)`

= – 96096

∴ the term independent of x is – 96096.

Concept: General Term in Expansion of (a + b)n
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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 3. (ii) | Page 80
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