Question

The Co-efficient of xⁿ in the expansion of (1+x) (1-x)ⁿ is

(a) (-1)^n-1 (n-1)² 

(b) (-1)ⁿ (1-n)

(c) n-1 

(d) (-1)^n-1n

Answer 1

Correct option: (– 1)ⁿ (1 – n)

Explanation:

given: (1 + x) (1 – x)ⁿ 

= [2 – (1 – x)] (1 – x)ⁿ 

= 2(1 – x)ⁿ – (1 – x)ⁿ⁺¹ 

∴ Coefficient of xⁿ = 2(– 1)ⁿ – ⁿ⁺¹c_n (– 1)ⁿ 

= (– 1)ⁿ [2 – {(n + 1)!} / (n!)}]

= (– 1)ⁿ [2 – n – 1]

= (– 1)ⁿ (1 – n)