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Question

In the polynomial (x - 1)(x - 2)(x - 3)............... .........(x - 100), the coefficient of x99 is


A

5050

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B

-5050

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C

100

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D

99

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Solution

The correct option is B

-5050


(x - 1)(x - 2)(x - 3)..............(x - 100)

Number of terms = 100;

∴ Coefficient of x99

= (x - 1)(x - 2)(x - 3)........(x -100)

= (-1 - 2 - 3 - .......... - 100) = -(1 + 2 +.........+ 100)

= - 100×1012 = - 5050.


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