5:
\(S=\dfrac{1}{2\cdot6}+\dfrac{1}{6\cdot10}+...+\dfrac{1}{98\cdot102}\)
\(=\dfrac{1}{4}\left(\dfrac{4}{2\cdot6}+\dfrac{4}{6\cdot10}+...+\dfrac{4}{98\cdot102}\right)\)
\(=\dfrac{1}{4}\left(\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{10}+...+\dfrac{1}{98}-\dfrac{1}{102}\right)\)
=1/4*100/204
=25/204