Question

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

Answer 1

Correct Answer - 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)`