In the polynomial (x - 1)(x - 2)(x - 3)............... .........(x - 100), the coefficient of x 99 is Options: A . &nbsp 5050 B . &nbsp -5050 C . &nbsp 100 D . &nbsp 99

In the polynomial (x - 1)(x - 2)(x - 3)............... .........(x

Question -

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

Options:

A . 5050

B . -5050

C . 100

D . 99

Answer: Option B
:
B

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

Number of terms = 100;

∴ Coefficient of $x^{99}$

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

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

= - $\frac{100 \times 101}{2}$ = - 5050.

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