If the sum of the coefficients in the expansion ${(1 + x - 3 x^{2})}^{171}$ is

- 3^{171}

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1

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2^{171}

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- 1

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Solution

The correct option is B $- 1$
$(1 + x - 3 x^{2})^{171}$
$= a_{0} + a_{1} x + a_{2} x^{2} . . .$ ...(i)
To get the sum of the coefficients we substitute $x = 1$ in (i)
Hence, we get
$a_{0} + a_{1} + a_{2} . . .$
$= (1 + 1 - 3 (1)^{2})^{171}$
$= (- 1)^{171}$
Since $171$ is odd, sum of coefficients $= (- 1)^{171} = - 1$

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