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`

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

We have, t_r+1 = ⁿC_r a^n–r .b^r

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

= ¹⁵C_rx^15–r.(–2)^r. x^–2r

= ¹⁵C_r (–2)^r x^15–3r

To get the term independent of x, we must have

x^15–3r= 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

Is there an error in this question or solution?

Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.3 | Q 3. (ii) | Page 80