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The sum of coefficient of integral power...

The sum of coefficient of integral powers of x in the binomial expansion of `(1-2sqrtx)^50` is:

A

`1/2(3^(50) + 1)`

B

`1/2(3^(50))`

C

`1/2(3^(50) - 1)`

D

`1/2(2^(10) + 1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1-2sqrt(x))^(50) = C_(0)-C_(1)2sqrt(x)+C_(2)(2sqrt(x))^(2)-"...."+C_(50)+(2sqrt(x))^(50)`
`(1+2sqrt(x))^(50) = C_(0) + C_(1)(2sqrt(x))+C_(2)(2sqrt(x))^(2) + "......" + C_(50)(2sqrt(x))^(50)`
Putting `x = 1`, we get
`:. (3^(50)+1)/(2)= C_(0) + C_(2)(2)^(2) + "...."`
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