#### 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.

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Solution for 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 . concept: General and Middle Terms. For the courses CBSE (Commerce), CBSE (Science), CBSE (Arts)