In the polynomial (x – 1)(x – 2)(x – 3) . . . . . .(x – 100), the coefficient of $x^{99}$ is

5050

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-5050

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100

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Solution

The correct option is B -5050
$(x - 1) (x - 2) (x - 3) \dots (x - 100)$
Number of terms = 100;
$∴$ Coefficient of $x^{99} = (x - 1) (x - 2) (x - 3) \dots (x - 100)$
$= (- 1 - 2 - 3 -_{\dots} - 100) = - (1 + 2 +_{\dots} + 100)$
$= - \frac{100 \times 101}{2} = - 5050$

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