Home
Class 12
MATHS
Coefficient of x^(2^(m+1)) in the expans...

Coefficient of `x^(2^(m+1))` in the expansion of `1/((1+x)(1+x^2)(1+x^4)(1+x^8).....(1+x^(2^m)))(|x|<1)` is

A

`0`

B

`1`

C

`2^(m)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `P=(1)/((1+x)(1+x^(2))(1+x^(4))(1+x^(8))....(1+x^(2^(m))))`
Multiplying the numerator and denominator by `1-x`, we have given expression
`=(1-x)/((1-x)(1+x)(1+x^(2))(1+x^(4))....(1+x^(2^(m))))`
`=(1-x)/((1-x^(2))(1+x^(2))(1+x^(4))....(1+x^(2^(m))))`
..........
...........
`=(1-x)/(1-x^(2^(m+1)))=(1-x)(1-x^(2^(m+1)))^(-1)`
`=(1-x)(1+x^(2^(m+1))+x^(2^(m+2))+...)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The coefficient of x^(n) in the expansion of ((1 + x)/(1-x))^(2), is

Find the coefficient of x^9 in the expansion of (1+x)(1+x^2)(1+x^3)(1+x^4)......(1+x^100)

The coefficient of x^24 in the expansion of (1+x^2)^(12) (1+x^12)(1+x^24) is

The coefficient of x^9 in the expansion of (1+x)(1+ x^2)(1+x^3)....(1+x^(100)) is

the coefficient of x^(r) in the expansion of (1 - 4x )^(-1//2) , is

The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3)) , is

The coefficient of x^4 in the expansion of ((1 -3x)^2)/((1 - 2x)) is

The coefficient of x^11 in the expansion of (1- 2x + 3x^2) (1 + x)^11 is

The coefficient of x^(48) in the expansion of (1+x^(4))(1+x^(24))(1+x^(48)) is

The coefficient of x^4 in the expansion of (1+x-2x^2)^7 is