If |x|<1, then the coefficient of x^n in...

If `|x|<1,` then the coefficient of `x^n` in expansion of `(1+x+x^2+x^3+)^2` is a. `n` b. `n-1` c. `n+2` d. `n+1`

A

n

B

n-1

C

n+2

D

n+1

Text Solution

Verified by Experts

The correct Answer is:

D

`(1+x+x^(2) +"…..")^(2) = ((1-x)^(-1))^(2) = (1-x)^(-2)`
`= 1+2x+3x^(2) + "…"`
Therefore, coefficient of `x^(n)` is `n+1`.

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