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Sum of the last $20$ coefficients in the expansion of ${(1 + x)}^{39}$ , when expanded in ascending power of $x$ is

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219

218

40C20−219

238

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detailed solution

Correct option is D

There are 40 terms in the expansion of 1+x39. Sum of the last 20 coefficients is S=39C20+39C21+…+39C38+39C39⇒ S=39C19+39C18+…+39C1+39C0 [Using nCr=nCn−r]Adding the above two expressions, we get 2S=39C0+39C1+…+39C39=239⇒ S=238

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Sum of the last 20 coefficients in the expansion of (1 + x)39, when expanded in ascending power of x is

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Sum of the last $20$ coefficients in the expansion of ${(1 + x)}^{39}$ , when expanded in ascending power of $x$ is