In the expansion of $(x - 1) (x - 2) . . . . (x - 18),$ the coefficient of $x^{17}$ is

684

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- 171

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171

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- 342

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Solution

The correct option is C $- 171$
$(x - 1) (x - 2) (x - 3) (x - 3) . . . . . . . . . . . . . . (x - 18)$

$= x^{18} - (1 + 2 + 3 + 4 + . . . . . . . . + 18) x^{17} + (1 \cdot 2 + 2 \cdot 3 + . . . . . . . . . . . + 18 \cdot 1) x^{16} - . . . . . . .$

So coefficient of $x^{17}$ is $= - (1 + 2 + 3 + . . . . . . . . + 18) = - \frac{18 \cdot 19}{2} = - 171$

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