In the expansion of [(1+x)//(1-x)]^2, th...

In the expansion of `[(1+x)//(1-x)]^2,` the coefficient of `x^n` will be `4n` b. `4n-3` c. `4n+1` d. none of these

A

`4n`

B

`4n-3`

C

`4n+1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A

Given term can be written as
`(1+x)^(2)(1-x)^(-2)=(1+2x+x^(2))[1+2x+3x^(2)+"....."+(n-1)xxx^(n-2)+nx^(n-1)+(n+1)x^(n)+"...."oo]`
Coefficient of `x^(n)` is `(n+1+2n+n-1)=4n`.

Promotional Banner

Promotional Banner

Topper's Solved these Questions

BINOMIAL THEOREM
CENGAGE|Exercise Exercise (Multiple)|27 Videos
BINOMIAL THEOREM
CENGAGE|Exercise Exercise (Comprehension)|20 Videos
BINOMIAL THEOREM
CENGAGE|Exercise Exercise 8.8|10 Videos
AREA UNDER CURVES
CENGAGE|Exercise Question Bank|10 Videos
CIRCLE
CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

Prove that the coefficient of x^n in the expansion of (1+x)^2n is twice the coefficient of x^n in the expansion of (1+x)^2n-1 .

In the expansion of (x^3-1/x^2)^n, n in N if sum of the coefficients of x^5 and x^(10) is 0 then n is

If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, is 28, then the sum of the coefficients of all the terms in this expansion, is : (1) 64 (2) 2187 (3) 243 (4) 729

In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coefficient is 64 and term with the greatest binomial coefficient exceeds the third by (n-1) , the value of x must be

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coefficient is ((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!) .

If the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,then coefficient of x^n is (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

If the sum of the coefficients in the expansion of (1 -3x + 10x^2)^(n) is a and the sum of the coefficients in the expansion of (1 - x^(2))^(n) is b , then

CENGAGE-BINOMIAL THEOREM-Exercise (Single)

The value of sum(r=0)^(50)(-1)^r(^(50)Cr)/(r+2) is equal to 1/(50xx51)...
Text Solution
|
sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...
Text Solution
|
sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...
Text Solution
|
The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...
Text Solution
|
Iff(x) =.^(40)C(1).x(1-x)^(39) + 2..^(40)C(2)x^(2)(1-x)^(38)+3..^(40)C...
Text Solution
|
If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...
Text Solution
|
In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...
Text Solution
|
Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...
Text Solution
|
sum(k=1)^ook(1-1/n)^(k-1)= n(n-1) b. n(n+1) c. n^2 d. (n+1)^2
Text Solution
|
The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...
Text Solution
|
1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+.... is equal to
Text Solution
|
1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) + "….." is equal to
Text Solution
|
If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is ...
Text Solution
|
Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)
Text Solution
|
If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...
Text Solution
|
If x is positive, the first negative term in the expansion of (1 + x)^...
Text Solution
|
If x is so small that x^(3) and higher power of x may neglected, then ...
Text Solution
|
If the expansion in power of x of the function (1)/(( 1 - ax)(1 - b...
Text Solution
|
If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)x^(2)+"….", the b sum(r=1)^(50...
Text Solution
|
If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h e na0+a1+a2++ar is equal to (...
Text Solution
|