# Find The Coefficient of X^99 ?

The coefficient of x^{99} in the expansion of (x-1) (x-2) (x-3) ……… (x-100) is

- 5050
- 5000
- -5050
- -5000

**Answer: (3) – 5050**

**Explanation:-
**(x – 1) (X – 2) (X – 3 ) (X – 4) ………….. (X – 100)

The number of terms = 100

Then, the coefficient of X^99

= (X – 1) (X – 2) (X – 3) …………………. (X – 99) (X – 100)

= ( – 1 – 2 – 3 – 4 – 5 ………………………. – 100)

= – (1 + 2 + 3 + ………………… + 100)

= – (100 x 101)/2

= – 101000/2

= – 5050

Then, the coefficient of X^99 is – 5050.

Hence, the answer is (3) – 5050.