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The coefficient of x^(1274) in the expan...

The coefficient of `x^(1274)` in the expansion of `(x+1)(x-2)^(2)(x+3)^(3)(x-4)^(4)…(x+49)^(49)(x-50)^(50)` is

A

`1275`

B

`-1275`

C

`-sum_(i=1)^(50)i^(2)`

D

`-sum_(i=1)^(50)i^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(x+1)(x-2)^(2)(x+3)^(3)(x-4)^(4)...(x+49)^(49)(x-50)^(50)`
Degree of the expression is `1+2+3+…+50=1275`
Coefficient of `x^(1274)` is `(1-2-2+3+3+3-4-4-4-4…)`
`=1^(2)-2^(2)+3^(2)-4^(2)+…+49^(2)-50^(2)`
`=-(1+2+3+..+50)`
`=-1275`
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