If `"|"x"}">1,` then expand `(1+x)^(-2)dot`

Answer

`(1)/(x^(2)) - (2)/(x^(3)) + (3)/(x^(4)) - (4)/(x^(5)) + "…"`

Explanation

Given that `|x| gt 1`.
So, the given expression can be written as
`x^(-2)(1+1/x)^(-2)=x^(-2)[1-2/x+3/(x^(2))-(4)/(x^(3))+"….."]`
`= [1/(x^(2))-(1)/(x^(3))+(3)/(x^(4))-(4)/(x^(5))+"…."]`