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

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

The coefficient of

x^{n}

in expansion of

(1+x)(1-x)^{n}

View answer and explanation

Correct option: B

(-1)^{n}(1-n)

Option B ((-1)^n(1-n)) is correct because it is the result of calculating the coefficient of x^n in the given expansion.

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n