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

  • Option 1)

    (-1)^{n-1}(n-1)^{2}\;

  • Option 2)

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

  • Option 3)

    \; (n-1)\;

  • Option 4)

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

 

Answers (1)

As we learnt in

Binomial Coefficients in Binomial Expansion -

In the expansion of \left ( x+a \right )^{n}, Binomial Coefficients are ^{n}c_{r}
 

- wherein

^{n}c_{r} is +ve .

\frac{n!}{r!\left ( n-r \right )!}

 

 Coefficient of xn in (1 + x) (1 - x)n

\Rightarrow\ \; (-1)^{n-1}\ ^{n}C_{n-1}+(-1)^{n}\ ^{n}C_{n}

\Rightarrow\ \; (-1)^{n}(1-n)

Correct option is 2.

 


Option 1)

(-1)^{n-1}(n-1)^{2}\;

This is an incorrect option.

Option 2)

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

This is the correct option.

Option 3)

\; (n-1)\;

This is an incorrect option.

Option 4)

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

This is an incorrect option.

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