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The coefficient of x^(n-2) in the polyno...

The coefficient of `x^(n-2)` in the polynomial `(x-1)(x-2)(x-3)...(x-n)` is

A

`(n(n^(2)+2)(3n+1))/(24)`

B

`(n(n^(2)-1)(3n+2))/(24)`

C

`(n(n^(2)+1)(3n+4))/(24)`

D

`(n(n^(2)-2)(3n-2))/(24)`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • Consider the expansion of ( 1+ x)^(2n+1) The coefficient of x^(99) in the expansion of (x-1) ( x-2) (x -3)"….." (x-100) is

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    D
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    A
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    B
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    C
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    D
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    B
    `((-1)^(n))/(n!) {n^(2)-n(a+1)-1}`
    C
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    D
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