Answer
$$\frac{5}{4},\quad \frac{205}{144}, \quad \frac{5369}{3600}.$$
Work Step by Step
We have
$$
S_{2}=1+\frac{1}{2^2}=1+\frac{1}{4}=\frac{5}{4},\\
S_{4}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}\\
=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}=\frac{205}{144},\\
S_{6}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}\\
=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}=\frac{5369}{3600}
$$
