Question

Prove that the coefficient of xⁿ  in the expansion of (1 + x)²ⁿ is twice the coefficient of xⁿ in the expansion of (1+x)^2n-1

Answer 1

In (1 + x)²ⁿ we have

From (1) and (2) we get, the coefficient of xn  in (1 + x)²ⁿ is twice the coefficient of xⁿ  in (1 + x)^2n-1.