Find The Coefficient of X^99 ?

The coefficient of x99 in the expansion of (x-1) (x-2) (x-3) ……… (x-100) is

  1. 5050
  2. 5000
  3. -5050
  4. -5000
Anurag Mishra Professor Asked on 30th September 2015 in Maths.
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1 Answer(s)

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.

Anurag Mishra Professor Answered on 3rd October 2015.
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