InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The coefficient of `x^99` in `(x-1)(x-2).....(x-100)` isA. 5050B. 5000C. -5050D. -5000 |
|
Answer» Correct Answer - C Coefficient of `x^(1)` in `[(x-1)(x-2)or(x^(2)-3x + 2)]` `=-3 =-1 - 2 =- (1+2)` Coefficient of `x^(2)` in `[(x-1)(x-2)(x-3)or(x^(3)-6x^(2)+5x-6)]` `=-6=-[1+2+3]`. Coefficient of `x^(3)` in `[(x-1)(x-2)(x-3)(x-4)or(x^(4)-10x^(3)-29x^(2)-11x + 24)]` `=-10=-[1+2+3+4]` `therefore` Coefficient of `x^(99)` in `[(x-1)(x-2)........(x-100)]` `=-[1+2+3+....+100]=(-100(100+1))/(2)=-5050`. |
|