Answer
The solution set is $\{ -\frac{1}{2},\frac{1}{8},-\frac{1}{26},\frac{1}{80} \}$.
Work Step by Step
The given expression is
$\frac{(-1)^n}{3^n-1}$
Plug $n=1$.
$=\frac{(-1)^1}{3^1-1}$
$=\frac{-1}{3-1}$
$=-\frac{1}{2}$.
Plug $n=2$.
$=\frac{(-1)^2}{3^2-1}$
$=\frac{1}{9-1}$
$=\frac{1}{8}$.
Plug $n=3$.
$=\frac{(-1)^3}{3^3-1}$
$=\frac{-1}{27-1}$
$=-\frac{1}{26}$.
Plug $n=4$.
$=\frac{(-1)^4}{3^4-1}$
$=\frac{1}{81-1}$
$=\frac{1}{80}$.
