The coefficient of $x^{17}$ in the expansion of $(x - 1) (x - 2) (x - 3) . . . (x - 18)$ is

164

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- 171

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194

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221

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Solution

The correct option is B $- 171$
The coefficient of $x^{17}$ is given by
$- 1 + (- 2) + (- 3) + . . . (- 18)$
$= - 1 - 2 - 3... - 18$
$= - (\frac{18 (18 + 1)}{2})$
$= - 9 (19)$
$= - 171$

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