Answer
$S_{2}$ = $\frac{2}{3}$
$S_{4}$ = $\frac{4}{5}$
$S_{6}$ = $\frac{6}{7}$
Work Step by Step
$S_{2}$ = $\frac{1}{1·2}+\frac{1}{2·3}$ = $\frac{2}{3}$
$S_{4}$ = $\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+\frac{1}{4·5}$ = $\frac{4}{5}$
$S_{6}$ = $\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+\frac{1}{4·5}+\frac{1}{5·6}+\frac{1}{6·7}$ = $\frac{6}{7}$
