Answer
The first five terms are:
$s_1 = \dfrac{1}{2};
\\s_2= \dfrac{2}{5};
\\s_3= \dfrac{2}{7};
\\s_4= \dfrac{8}{41};
\\s_5= \dfrac{8}{61}$
Work Step by Step
Substitute $n=1, 2, 3, 4, 5$ to obtain:
$s_1 = \dfrac{2^1}{3^1+1}=\dfrac{2}{4} = \dfrac{1}{2};
\\s_2= \dfrac{2^2}{3^2+1}=\dfrac{4}{10} = \dfrac{2}{5};
\\s_3= \dfrac{2^3}{3^3+1}=\dfrac{8}{28} = \dfrac{2}{7};
\\s_4= \dfrac{2^4}{3^4+1}=\dfrac{16}{82} = \dfrac{8}{41};
\\s_5= \dfrac{2^5}{3^5+1}=\dfrac{32}{244} = \dfrac{8}{61}$