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Find the coefficient of x^99 in the expansion of (x+1)(x+2)(x+3)...(x+100).

Find the coefficient of x^99 in the expansion of (x+1)(x+2)(x+3)...(x+100).

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
Given polynomial:

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

= x100 + (1 + 2 + 3 + . . . . . . . + 100) x99 + (. . .) x98 + . . . . . .

Here coeff. Of x99 = (1 + 2 + 3 + . . . . . . .+ 100)

= 100 x 101/2 = 5050.
 
 
Regards
Arun (askIITians forum expert)

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