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If "|"x"|">1, then expand (1+x)^(-3)dot...

If `"|"x"|">1,` then expand `(1+x)^(-3)dot`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(x^(2)) - (2)/(x^(3)) + (3)/(x^(4)) - (4)/(x^(5)) + "…"`
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))+"…."]`
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