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Property 7

If 1+x n =...

Question

If ${(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . + C_{n} x^{n}$ , then $C_{0} - C_{1} + C_{2} - C_{3} + . . . + {(- 1)}^{n} . C_{n}$ is equal to:

A

3^{n}

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B

2^{n}

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C

1

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D

0

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Solution

The correct option is C $0$
Given,
${(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . + C_{n} x^{n}$
Put $x = - 1$ , we get
$C_{0} - C_{1} + C_{2} - . . . + {(- 1)}^{n} . C_{n} = 0$

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