The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/...

The sum of `1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo` will be `x^n` b. `x^(-n)` c. `(1-1/x)^n` d. none of these

A

`x^(n)`

B

`x^(-n)`

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A

`1+n(1-1/x) + (n(n+1))/(2!) (1-1/x)^(2)+"…."oo`
`= 1-n[-(1-1/x)]+(-n(-n-1))/(2!)[-(1-(1)/(x))]^(2)+"....."oo`
`= [1-(1-(1)/(x))]^(-n)`
`= x^(n)`

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