In the expansion of $(1 + x)^{n}$ , the sum of coefficients of odd powers of $x$ is

2^{n} + 1

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2^{n} - 1

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2^{n}

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2^{n - 1}

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Solution

The correct option is C $2^{n - 1}$
${(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3} + . . . + C_{n} x^{n}$
Putting $x = 1$ and $x = 1$ and subtracting, we get.
$2^{n} = 2 (C_{1} + C_{3} + C_{5} + . . .)$
$∴ C_{1} + C_{3} + C_{5} + . . . = 2^{n - 1}$
Or the sum of the coefficients of the odd power of $x$ is $2^{n - 1}$

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