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CGP EDU Academic Team
Published on: August 14, 2026
Prove that the coefficient of the middle term in the expansion of (1 +x) 2n is the sum of the coefficient of the two middle terms in the expansion (1 + x) 2n –1
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Sol. In (1+x) 2n middle term is (n + 1) coeff. of T n + 1
= 2n C n ... (1)
In (1 + x) 2n – 1 there are two m.t. which are n th & (n + 1) th
coeff. of T n = 2n–1 C n–1 , Coeff. of T n + 1 = 2n–1 C n
Now 2n– 1 C n –1 + 2n–1 C n = 2n C n Hence proved
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