The coefficient of x^(18) in the produc...

The coefficient of `x^(18)` in the product `(1+x)(1-x)^(10)(1+x+x^(2))^(9)` is k. The value of `(k)/(12)` is __________.

Verified by Experts

The correct Answer is:

7

`(1+x)(1-x)^(10)(1+x+x^(2))`
`(1-x^(2))(1-x^(3))^(9)=.^(9)C_(6)(x^(3))=(9xx8xx7)/(3xx2)=84`

Similar Questions

Explore conceptually related problems

The coefficient of x^(18) in the expansion (1+x)(1-x)^(10)(1+x+x^(2))^(9) is

The coefficient of x^(70) in the product (x-1)(x^(2)-2)(x^(3)-3)dots(x^(12)-12) is

The coefficient of x^(9) in the expansion of E = (1 + x)^(9) + (1 + x)^(10) + ... + (1 + x)^(100) is

Find the coefficient of x^(k) in 1+(1+x)+(1+x)^(2)+...+(1+x)^(n)(0<=k<=n)

Find the coefficient of x^(k)in 1+(1+x)+(1+x)^(2)+...+(1+x)^(n)(0<=k<=n)

The coefficient of x^(m) in (1+x)^(k)+(1+x)^(k+1)+....+(1+x)^(n),(k<=m<=n) ,is given by

Coefficient of x^(13) in the expansion of (1-x)^(5)(1+x+x^(2)+x^(3))^(4)(1+x^13)^(8) is k then k+6 is equal to

Find the coefficient of x^(-2) in (1+x^(2)+x^(4)) (1-1/(x^(2)))^(18)

If HCF of (x^(2)+x-12) and (2x^(2)-kx -9) is (x-k) , then value of k is