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If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(...

If `|x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+......` is equal to a.`((2x)/(1+x))^n` b. `((1+x)/(2x))^n` c. `((1-x)/(1+x))^n` d. `((1+x)/(1-x))^n`

A

`((2x)/(1+x))^(n)`

B

`((1+x)/(2x))^(n)`

C

`((1-x)/(1+x))^(n)`

D

`((1+x)/(1-x))^(n)`

Text Solution

Verified by Experts

The correct Answer is:
D
Required value of
`(1-(2x)/(1+x))^(-n) = ((1+x-2x)/(1+x))^(-n) = ((1-x)/(1+x))^(-n) = ((1+x)/(1-x))^(n)`
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