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The coefficient of x^(53) in the expansi...

The coefficient of `x^(53)` in the expansion of `sum_(m=0)^(100) ^100C_m(x-3)^(100-m) 2^m` is equal to

A

`.^(100)C_(47)`

B

`.^(100)C_(53)`

C

`-.^(100)C_(53)`

D

`-.^(53)C_(100)`

Text Solution

Verified by Experts

The correct Answer is:
C
The given sigma is the expansion of
`[(x-3)+2]^(100)=(x-1)^(100)= (1-x)^(100)`
Therefore, `x^(53)`will occur in `T_(54)`.
Therefore, the coefficient is `-.^(100)C_(53)`.
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