Question

If (1+ x + x²)ⁿ = a₀ + a₁x + a₂x² + . . . + a_2nx²ⁿ, then a₀ + a₃ + a₆ + a₉ + .....is equal to 

(A)  3ⁿ 

(B)  3ⁿ⁻¹

(C)  3ⁿ⁺¹ 

(D)  None of these

Answer 1

Correct option (B)  3ⁿ⁻¹

(1 + x + x²)ⁿ = a₀ + a₁x + a₂x² + … + a_2nx²ⁿ

Putting x = 1, ω, ω² in turn we get

3ⁿ = a₀ + a₁ + a₂ + a₃ + … + a_{2n ...} (1)

0 = a₀ + a₁ω + a₂ω₂ + …+ a_2nω²ⁿ ...(2)

and  0 = a₀ + a₁ω² + a²ω⁴ + … + a_2nω²ⁿ  ...(3)

Adding Eqs. (1), (2) and (3)

Comments

Good logic