The coefficient of xn in expansion of 1-x1-xn isA- -1n-1n-12B- -1n1-nC- n 1 D- -1n-1 n

The correct option is B (1+x)(1 x)^n=(1+x)(^nC_0 ^nC_1 x+^nC_2x^2+⋯+( 1)_n)^nC_n) Coefficient of x^n is( 1)^n ^nC_n +( 1)^n 1 ^nC_n 1 =( 1)^n(1 n) ...

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Byju's Answer

Standard XII

Mathematics

Sum of Coefficients of All Terms

The coefficie...

Question

The coefficient of $x^{n}$ in expansion of $(1 + x) (1 - x)^{n}$ is

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Solution

The correct option is D

$(1 + x) (1 - x)^{n} = (1 + x) (^{n} C_{0} -^{n} C_{1} x +^{n} C_{2} x^{2} + \dots + (- 1)_{n})^{n} C_{n})$ $C o e f f i c i e n t o f x^{n} i s (- 1)^{n}$ $^{n} C_{n}$ $+ (- 1)^{n - 1}$ $^{n} C_{n - 1}$ $= (- 1)^{n} (1 - n)$

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The coefficient of xn in expansion of (1+x)(1–x)n is

The correct option is D (1+x)(1−x)n=(1+x)(nC0−nC1 x+nC2x2+⋯+(−1)n)nCn) Coefficient of xn is(−1)n nCn +(−1)n−1 nCn−1 =(−1)n(1−n)

The coefficient of $x^{n}$ in expansion of $(1 + x) (1 - x)^{n}$ is

The correct option is D

$(1 + x) (1 - x)^{n} = (1 + x) (^{n} C_{0} -^{n} C_{1} x +^{n} C_{2} x^{2} + \dots + (- 1)_{n})^{n} C_{n})$ $C o e f f i c i e n t o f x^{n} i s (- 1)^{n}$ $^{n} C_{n}$ $+ (- 1)^{n - 1}$ $^{n} C_{n - 1}$ $= (- 1)^{n} (1 - n)$