Question

in the expansion of (x-1/X)^6 the constant term is

Answer 1

hope it helps....... :)

Answer 2

In the expansion of (x - 1/x)⁶, the constant term is (- 20).

Step-by-step explanation:

Let the (r + 1)th term of the expansion is the constant term.

Then the (r + 1)th term is

= ⁶Cᵣ . x⁶ ⁻ ʳ . (- 1/x)ʳ

= ⁶Cᵣ . (- 1)ʳ . x⁶ ⁻ ʳ ⁻ ʳ

= ⁶Cᵣ . (- 1)ʳ . x⁶ ⁻ ²ʳ

So 6 - 2r = 0 or, r = 3

Thus the 4th term of the expansion is

= ⁶C₃ . (- 1)³

= 20 . (- 1)

= - 20

∴ the constant term of the expansion is (- 20).

Method explanation:

- consider the (r + 1)th term to be the constant term.

- in the expression of (r + 1)th term, equate the exponent of x with zero.

- find the value of r.

- replace r in the expression of (r + 1)th term.

Homeworks for you:

1. Find the constant term in the expansion of (3x²/2 - 1/3x)⁹ [ Ans. 7/18 ]

2. If the (r + 1)th term of the expansion of (x³ - 3/x²)¹⁵ is of no x, find r. [ Ans. r = 9 ]