Answer
No, he's not correct.
$n=\frac{s}{1-s}$, not $\frac{s}{s-1}$
Work Step by Step
$s=\frac{n}{n+1}$
$s(n+1)=n$
$sn+s=n$
$s=n-sn$
$s=n(1-s)$
$\frac{s}{1-s}=n$
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