State TRUE or FALSE
$[1 - (1 - (1 - n)^{- 1})^{- 1}]^{- 1}$ , then the answer is n

True

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False

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Solution

The correct option is A True
As given
$\Rightarrow [1 - (1 - (1 - n)^{- 1})^{- 1}]^{- 1}$
$\Rightarrow {[1 - {(1 - (\frac{1}{1 - n}))}^{- 1}]}^{- 1}$
$\Rightarrow {[1 - {(1 - \frac{1}{1 - n})}^{- 1}]}^{- 1}$
$\Rightarrow {[1 - {(\frac{1 - n - 1}{1 - n})}^{- 1}]}^{- 1}$
$\Rightarrow {[1 - {(\frac{- n}{1 - n})}^{- 1}]}^{- 1}$
$\Rightarrow {[1 - (\frac{1 - n}{- n})]}^{- 1}$
$\Rightarrow {[1 - \frac{1 - n}{- n}]}^{- 1}$
$\Rightarrow {[\frac{- n - 1 + n}{n}]}^{- 1}$
$\Rightarrow {[\frac{- 1}{- n}]}^{- 1} \Rightarrow + n$

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