Home
Class 11
MATHS
The sum of coefficients in integral powe...

The sum of coefficients in integral powers of x in the binominal expansion `(1 - 2 sqrt(x))^(50)` is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
c
We observe that only the odd terms in the
binomial expansion of `(1-2sqrt(x))^(50)` contain integral powers of x.
Also,
`(1 + 2 sqrt(x))^(50) + (1 - 2sqrt(x))^(50)`
`= 2 {""^(50)C_(0) + ""^(50)C_(1) (2 sqrt(x))^(2) + ""^(50)C_(4) (2sqrt(x))^(4) + ... +""^(50)C_(50)(2 sqrt(x))^(50)}` Replacing c by 1 on both side, we obtain
`3^(50) + (-1)^(50) = 2 {""^(50)C_(0) + ""^(50)C_(1) (2)^(2) + ""^(50)C_(4) (2)^(4) + ... +""^(50)C_(50)(2)^(50)}`
`rArr (1)/(2) (3^(50) +1)` = Sum of the coefficeints of integral power of x.
Promotional Banner

Similar Questions

Explore conceptually related problems

The sum of coefficients of integral powers of x in the binomial expansion of (1-2sqrt(x))^(50) is: (1) (1)/(2)(3^(50)+1)(2)(1)/(2)(3^(50))(3)(1)/(2)(3^(50)-1)(4)(1)/(2)(2^(50)+1)

Find the sum of the coefficients of all the integral powers of x in the expansion of (1+2sqrt(x))^(40)

Sum of the last 30 coefficients of powers of x in the binomial expansion of (1 + x)^(59) is:

The sum of the coefficients of even powers of x in the expansion (1-x+x^(2)-x^(3))^(5) is

The sum of the coefficients of odd powers of x in the expansion (1+x+x^(2)+x^(3))^(5)

The sum of the coefficients of even power of x in the expansion of (1+x+x^(2)+x^(3))^(5) is 256 b.128c.512d.64

The sum of the co-efficients of all the even powers of x in the expansion of (2x^(2)-3x+1)^(11) is -