Question

The term independent of x in the expansion of

(1 + x)ⁿ (1 + 1/x)ⁿ is -

• A. C₀² + 2C₁² + 3C₂²+ .... + (n + 1) C_n²
• B. (C₀ + C₁ + ..... + C_n)²
• C. C₀² + C₁²+ .... + C_n²
• D. None of these

Answer 1

Answer: (C)

C₀² + C₁²+ .... + C_n²

Answer 2

We have

(1 + x)ⁿ $\left( 1 + \frac{1}{x} \right)^{n}$= (C₀ + C₁x + C₂x² + ...... + C_nxⁿ)

× $\left( C_{0} + \frac{C_{1}}{x} + \frac{C_{2}}{x^{2}} + ..... + \frac{C_{n}}{x^{n}} \right)$

Term independent of x on the R.H.S.

= C₀² + C₁² + C₂² +.....+ C_n² .