Answer
The answer is $\left \{ \frac{1}{3}, -\frac{1}{5}, \frac{1}{9}, -\frac{1}{17}\right \}$.
Work Step by Step
The given general term is
$a_n=\frac{(-1)^{n+1}}{2^n+1}$
For the first term plug $n=1$.
$a_1=\frac{(-1)^{1+1}}{2^1+1}$
$a_1=\frac{(-1)^{2}}{2+1}$
$a_1=\frac{1}{3}$.
For the second term plug $n=2$.
$a_2=\frac{(-1)^{2+1}}{2^2+1}$
$a_2=\frac{(-1)^{3}}{4+1}$
$a_2=\frac{-1}{5}$.
For the third term plug $n=3$.
$a_3=\frac{(-1)^{3+1}}{2^3+1}$
$a_3=\frac{(-1)^{4}}{8+1}$
$a_3=\frac{1}{9}$.
For the fourth term plug $n=4$.
$a_4=\frac{(-1)^{4+1}}{2^4+1}$
$a_4=\frac{(-1)^{5}}{16+1}$
$a_4=\frac{-1}{17}$.
Hence, the first four terms are
$\left \{ \frac{1}{3}, -\frac{1}{5}, \frac{1}{9}, -\frac{1}{17}\right \}$.
