#### Question

Prove that the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n} is twice the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n}^{–1 }.

#### Solution

Comparing the indices of *x* in *x*^{n} and in *T*_{r}_{ + 1}, we obtain

*r* =* n*

Therefore, the coefficient of* x*^{n} in the expansion of (1 + *x*)^{2}^{n} is

Therefore, the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n} is twice the coefficient of *x*^{n} in the expansion of (1 + *x*)^{2}^{n}^{–1}.

Hence, proved.

Is there an error in this question or solution?

Solution 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 . Concept: General and Middle Terms.