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

5050

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- 5050

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100

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99

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Solution

The correct option is B $- 5050$
$c o e f f i c i e n t o f x^{99} w i l l b e = - (s u m o f a l l z e r o e s) = - [1 + 2 + 3 + . . . . . . . + 100] = - (\frac{100}{2}) [2 + (100 - 1) \cdot 1] = - 50 \cdot 101 = - 5050$

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