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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 .

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It is known that (r + 1)th term, (Tr+1), in the binomial expansion of (a + b)n is given by

Assuming that xn occurs in the (r + 1)th term of the expansion of (1 + x)2n, we obtain

Assuming that xn occurs in the (k +1)th term of the expansion (1 + x)2n – 1, we obtain

Therefore,

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.

Hence, proved.

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