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Sum of Binomial Coefficients of Odd Numbered Terms

In the expans...

Question

In the expansion of $(1 + x)^{70}$ , the sum of coefficients of odd powers of x is

A

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B

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C

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D

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Solution

The correct option is B
Fact. The sum of the coefficients of odd powers in the expansion of $(1 + x)^{n}$ =sum of the coefficients of even powers in $(1 + x)^{n}$
$= 2^{n - 1}$
$2^{70 - 1} = 2^{69}$

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